A function and a quadrant are given. Find the other five function values. Give exact answers.
Answers
The other five function values are sin(Ф)= -4/5, tan(Ф)= 4/3, cot(Ф)= 3/4, sec(Ф)= -5/3 and csc(Ф)= -5/4.
what is trigonometry?Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. Trigonometry has a wide variety of identities. With the intention of simplifying an expression, finding a more practical form of an expression, or solving an equation, these trigonometric identities are frequently employed to rewrite trigonometrical expressions.Since x is in IIIrd quadrant sin and cos will be negative but tan will be positive
given cos x= -3/5
We know that
sin²x + cos²x=1
sin²x+(-3/5)²=1
sin²x+9/25=1
sin²x=1-9/25
sin²x=16/25
sinx= ±√16/25
sinx= ±4/5
since, x is in IIIrd quadrant.
As sinx is negative IIIrd quadrant,
∴sinx= -4/5
tanx=sinx/cosx
=-4/5÷-3/5
=4/3
cotx=1/tanx
=1/4/3
=3/4
cosecx=1/sinx
=1/-4/5
=-5/4
secx=1/cosx
=1/-3/5
=-5/3
Hence, The other five function values are sin(Ф)= -4/5, tan(Ф)= 4/3, cot(Ф)= 3/4, sec(Ф)= -5/3 and csc(Ф)= -5/4.
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Related Questions
Help me please in need of it
Answers
Answer:
-2
Step-by-step explanation:
Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).
Image below to be answered
Answers
a.The formula that describe the sequence or progression is a+(7-7n)
b. 2nd term = -10 , 3rd term = 10, 4th term = -10 and 5th term = 10
What is arithmetic and geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
The nth term of an arithmetic progression is given as a(n)= a + (n − 1) × d
In geometric progression the nth term is given as a(n)= ar^(n-1)
where a is the first term
therefore if a = 12 and d is - 7
the formula for the arithmetic progression =
a(n) = 12+(n-1) -7 = 12+( 7-7n)
If the first term of a GP is 10 with common ratio of -1
then the second term = 10×-1 = -10
third term = -10×-1 = 10
fourth term = 10×-1 = -10
fifth term = -10× -1 = 10
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consider a two-factor factorial design with three levels for facts a, three levels for factor b, and four replicates in each of the nine cells
a. how many degrees of freedom are there in determining the A variation and the factor B variation
b. how many degrees of freedom are there in dreaming the interaction variation
c. how many degrees of freedom are there in determining the random variation
d. how many degrees of freedom are there in determining the total variation
Answers
In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.
What is a two-factorial design?A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.
Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.
From the data given:
a.
In calculating the factor A variation, there are two degrees of freedom.
In determining the variation of factor B, there are two degrees of freedom.
b.
Finding the degree of freedom using the interaction variation, there are four degrees of freedom.
c.
In finding the random variable, there are 9(4-1) = 27 degrees of freedom.
d.
In calculating the total variable, there are 9*4-1 =35 degrees of freedom.
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If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options.
Answers
Answer:
Step-by-step explanation:
the first ine make sense to me
if not right sorry
Answer:
0.5in and 2in
Step-by-step explanation:
It is the answer
Find the mean, median, and mode(s) of the data. Choose the measure that best represents the data. 31, 35, 2, 32, 27, 35
Please Answer Quickly :^)
Answers
median : 31.5
mode : 35
A plane flew a total of 1920 miles at the average rate of speed of 320 mph. How long did it take the plane to cover this distance?
Use the formula: D = r • t
Answers
Answer:
t = 6 hours
Step-by-step explanation:
D = r x t
1920 = 320t
divide both sides by 320:
t = 6 hours
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $3500 per month. You have access to an account that pays an APR of 4.8% compounded monthly. This requires a nest egg of $610,823.48.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)
Answers
The monthly deposit that is required to achieve the desired monthly yield at retirement is $1,056.71.
What is the monthly deposit?An annuity is a series of payment that is made over a period of time. The annuity in this question would last for 25 years. When an investment is compounded monthly, it means that the investment would grow at an exponential rate once in a month.
The formula that would be used to determine the monthly payment is:
Monthly payment = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = monthly interest rate = 4.8% / 12 = 0.4%n = number of periods = number of compounding x number of years: 12 x 25 = 300$610,823.48 ÷ [{(1.004^300) - 1} / 0.004] = $1,056.71
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work out the sale has been decreased
20% of 120
Answers
The current amount of the sale is 96
How to find the current amount of the sale ?The sale is 120
It was decreased by 20%
20/100 × 120
= 0.2 × 120
= 24
The amount of the current sale is
120-24
= 96
Hence the amount of the current sale which is calculated by subtracting 24 from 120 is 96
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Divide X^2-14x+45 by x-9
Answers
Answer:
x + 5
Step-by-step explanation:
Answer: \($x-5$\)
Step-by-step explanation:
Factoring \($x^2-14x+45$ gives us $(x-9)(x-5)$. Cancelling we get our desired answer, $\boxed{x-5}$.\)
El mayor es Novecientos mil cuatrocientos ochenta y nueve , y cuarenta mil dos
Answers
El número "Novecientos mil cuatrocientos ochenta y nueve" se representa como 900,489 en notación numérica.
Por otro lado, el número "cuarenta mil dos" se representa como 40,002.
Si estamos buscando determinar cuál de estos dos números es mayor, podemos comparar las cifras en cada posición.
Comenzando desde la izquierda, el primer dígito de 900,489 es 9, mientras que el primer dígito de 40,002 es 4.
Dado que 9 es mayor que 4, podemos concluir que 900,489 es mayor que 40,002.
En general, al comparar números, se debe observar cada posición en orden de mayor a menor importancia.
Esto significa que el primer dígito a la izquierda es el más significativo y tiene más peso en el valor total del número.
Si los dígitos en la posición más significativa son iguales, se debe pasar a la siguiente posición hasta que se encuentre una diferencia.
En este caso, dado que el primer dígito de 900,489 es mayor que el primer dígito de 40,002, no es necesario comparar los dígitos en posiciones posteriores.
Por lo tanto, podemos concluir que el número "Novecientos mil cuatrocientos ochenta y nueve" (900,489) es mayor que "cuarenta mil dos" (40,002).
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(c)yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) (d) x2 dx-xy dy + dz, where c is the parabola z = x2, y = 0 from (-1, 0, 1) to (1, 0, 1)
Answers
The value of the line integral is 1/2.
To evaluate this line integral, we need to parameterize the curve C that consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1).
Let's parameterize the first segment from (1,0,0) to (0,1,0) using t as the parameter
r(t) = (1-t) * <1,0,0> + t * <0,1,0>
= <1-t, t, 0>
where 0 ≤ t ≤ 1.
Now, let's parameterize the second segment from (0,1,0) to (0,0,1) using s as the parameter
r(s) = (1-s) * <0,1,0> + s * <0,0,1>
= <0, 1-s, s>
where 0 ≤ s ≤ 1.
We can then use the parameterization of C to evaluate the line integral:
∫_c yz dx + xz dy + xy dz
= ∫_0^1 yz dx/dt dt + xz dy/dt dt + xy dz/ds ds
= ∫_0^1 (t(1-t)) 0 dt + ((1-t)t) 0 dt + ((1-t)t) ds
= ∫_0^1 (1-t)t ds
= 1/2
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The given question is incomplete, the complete question is:
∫_c yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) Evaluate Line Integrals
Evaluate the expression for q = 5: q +8.9
Answers
The expression q = 5:q +8.9 has no parenthesis, so we will use the Order of Expression next. After parenthesis, we have to evaluate multiplication and division, so the given expression is equivalento of:
\(q=\frac{5}{q}+8.9\)Now, we can start by multiplying both sides by "q":
\(\begin{gathered} q^2=5+8.9q \\ q^2-8.9q-5=0 \end{gathered}\)We have got a quadratic equation and we need to find its zero, so we can use the quadratic formula:
\(\begin{gathered} q=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{8.9\pm\sqrt[]{(-8.9)^2-4\cdot1\cdot(-5)}}{2\cdot1} \\ q=\frac{8.9\pm\sqrt[]{79.21+20}}{2}=\frac{8.9\pm\sqrt[]{99.21}}{2} \\ q\approx\frac{8.9\pm9.96}{2} \end{gathered}\)Now, we will have two answers:
\(q_1\approx\frac{8.9+9.96}{2}=\frac{18.86}{2}=9.43\)And:
\(q_2=\frac{8.9-9.96}{2}=\frac{-1.06}{2}=-0.53\)So, the solutions for the equation are 9.43 and -0.53.
Luca cut 5 shelves of equal length using 1/2 of a yard of wood. How long was each shelf?
Answers
Each shelf was 1/10 of a yard long.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
Given that Luca cut 5 shelves of equal length using 1/2 of a yard of wood
There were 5 shelves.
1/2 divided by 5
⇒ (1/2)/5
⇒ (1/2)/(5/1)
⇒ (1/2)(1/5)
⇒ 1/10
Hence, each shelf was 1/10 of a yard long.
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Which triangle is a translation of triangle P? On a coordinate plane, triangle P is shifted 5 units to the right and 7 units up to form triangle C. triangle A triangle B triangle C triangle D Mark this and return
Answers
Answer: Triangle C.
Step-by-Step Explanation:
To solve this problem, we need to understand what it means for a triangle to be a translation of another triangle. A translation for a triangle means that it is the same shape and size as the original triangle, but it has shifted (or moved) a specific number of units either up, down, left, or right.
In this problem, we have Triangle P, which has been shifted 5 units to the right and 7 units up to form Triangle C. To determine which triangle is a translation of Triangle P, we can look at the coordinates of the different triangles.
Triangle A: (1, 4), (3, 7), (5, 6)
Triangle B: (2, 3), (4, 6), (6, 5)
Triangle C: (6, 11), (8, 14), (10, 13)
Triangle D: (3, 5), (5, 8), (7, 7)
If we compare the coordinates of each triangle with those of Triangle P, we can see that Triangle C, with coordinates (6, 11), (8, 14) and (10, 13), is the translation of Triangle P because all of the coordinates of Triangle P have been shifted 5 units to the right, and 7 units up. Therefore, the answer is Triangle C.
the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answers
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
Please help!!!! It’s urgent
Which of the following rational functions is graphed below?
-10
10-
-10
1
A. F(x) = 1/x(x+3)
B. F(x)= x/x+3
C. F(x)= 3/x
D. F(x)= 1/x(x-3)
Answers
Answer:
the answer is D. F(x) = 1/x(x-3)
Step-by-step explanation:
Write the equation of the graphed circle.
Answers
What graph is produced from the following function: f(x)= 1/4x
Answers
Answer:
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
The graph is of all the points such that y is 1/4 of x. So, for x=4, y=1, for example. Similarly, for x=-4, y=-1.
These, (4, 1) and (-4, -1), are two points on the graph, which is a straight line through those points and through the origin. The graph extends to infinity to the lower left and the upper right. A portion is shown below.
An object travels along a horizontal straight path at a constant rate. The object travels 1/20 of the length of the path in 3/4 second. At that rate, how many seconds does it take the object to travel the entire length of the path?
Please explain how u got the answer
A. 15 3/4
B. 20 3/4
C. 20
D. 15
Answers
Answer:
Below.
Step-by-step explanation:
1/20 is a small distance needed to be traveled right?
20/20 is the whole length.
If 1/20 gets traveled in 3/4 of a second,
3/4x2- or 2(1/20) which equals one right?
20(3/4) = 15 seconds
Just need the answer
Answers
Answer:
It seems no one can eat just one potato ship
Step-by-step explanation:
What is 5^-3?
Please I really need someone to explain to me what do you do when there is a negative sign in the exponent. Thank you :)
Answers
You take out the negative and do the regular equation but turn it into the fraction with one as the numerator and the solution of the exponent as the denominator.
Answer: 1/125 or 0.008 (simplify 1.125 or should I do it?)
Step-by-step explanation:
Well, when there is a negative sign in the exponent you only move the negative exponents. Moving only negative exponents is recommended because using this rule, you multiply two exponents with the same base and add their powers.
Solve by graphing x-2y=4. X+3y=14 the y-coordinate of the solution is y=?
Answers
The y-coordinate of the solution of the equation will be 2.
Given that:
x - 2y = 4
x + 3y = 14
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
If the slopes are different then the lines are intersecting.
And if the slopes are different then the system has one solution.
The lines are drawn on the graph and their intersection point will be (8, 2).
The y-coordinate of the solution of the equation will be 2.
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what contribution to geometry is attributed to the work of rene descartes
Answers
The contribution to geometry that the work of Rene Descartes is credited with is inventing analytic geometry.
What did Rene Descartes do ?Rene Descartes is frequently referred to as the creator of analytic geometry, a branch of geometry and algebra. This is due to Descartes' discovery that any two-dimensional point may be plotted on a mathematical plane.
Descartes traveled throughout northern and southern Europe from 1619 to 1628, where, as he subsequently claimed, he studied "the book of the world." He made his name by creating analytic geometry while he was in Bohemia in 1619.
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Jacque is using an unopened soup can for a school project and wants to paint it. If the can is 10 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14.
1,073.88 cm2
635.85 cm2
621.72 cm2
409.77 cm2
Answers
The amount of paint needed for the soup can is 409.77 cm².
How to find the surface area?Jacque is using an unopened soup can for a school project and wants to paint it.
The can is 10 cm tall and has a diameter of 9 cm. Therefore, the square centimetres of paint required to paint the soup is as follows:
Therefore,
surface area of a cylinder = 2πr(r + h)
where
r = radiush = heightTherefore,
r = 9 / 2 = 4.5 cm
h = 10 cm
surface area of a cylinder = 2 × 3.14 × 4.5(4.5 + 10)
surface area of a cylinder = 28.26(14.5)
surface area of a cylinder = 409.77 cm²
Therefore,
amount of paint needed = 409.77 cm²
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pls help me with this
Answers
Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.
An unitary method is what ?The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.
Here,
=> A = L x W,
where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.
Inputting the numbers provided yields:
=> A = (7/4) x (1/3)
These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.
The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:
=> A = (7 x 1) / (4 x 3)
When we multiply the numerator by the remainder, we obtain:
=> A = 7/12
The rectangle's size is 7/12 square inches as a result.
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The revenue for Company A was $239 million, compared to $467 million for Company B. The revenue for Company A was ____% of the revenue for Company B. (Round to the nearest tenth as needed.)
Answers
Company A's revenue was $239 million whereas Company B's was $467 million as a result revenue for Company A was equal to 52% of that for Company B.
What is the percentage?It shows the proportion between two integers when stated as a decimal fraction of 100 parts. It is a statistic used to compare two sets of data, and the sign % is used to represent it as a percentage.
It is given that, the revenue for Company A was $239 million, compared to $467 million for Company B.
We have to find the % by which A was revenue for Company B.
Suppose x% by which A was revenue for Company B.
⇒$467 of x =$239
⇒467×x=239
⇒x=239/467
⇒x=0.5177 ≈ 0.52
⇒x%=52%
Thus, the revenue for Company A was equal to 52% of that for Company B.
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Identify the Input values: (0,2), (1,3), (5,9), (7,13) *
Answers
Reposted, please help!!!
Answers
Step-by-step explanation:
DNE!
HOPE ITS RIGHT....
Estimate the sum of 379+409=
Answers
Answer:
Round both numbers to 1 significant figure.
400+400=800
800 is the answer.
I have no more points so please help me with this question -In a scatter plot that shows a positive association, describe how y-values change as x-values increases.
Answers
Answer:
As the x-values increase, the y- value tend to decrease.
Step-by-step explanation: