Use the range given for theta to determine solutions to each equation Sin(theta) = (1/3), 0 < or equal to (theta) < or equal to (pi)

Q: Find all solutions of the equation sin x = 0.

A: The given equation is  sin x = 0.

Q: What is the range of the sine function?

A: We know, domain of sine function is all real numbers. Also, -1≤sinx≤1 ⇒range of sinx is [-1,1].

Q: 2 tan x+11=

A:

Q: Find the exact solutions of the equation in the interval [0, 2x). tan(2x) – cot(x) = 0

A: In order to find the values transform the equation on the left side equation in a single…

Q: Reduce sin 0 to an expression involving only function of multiples of 0, raised to the first power.

A: Given, sin4θ  We have to reduce sin4θ to an expression involving only function of multiples of θ,…

Q: Find a value of x that satisfies the equation sin 58° cos (x). %3D

A: Use the trigonometric identities and simplify.

Q: Find the exact value of the expression whenever it is defined.

A: Definition used -                       Domain of sin-1(x) is [-1,1].                       Range of…

Q: sin 4

A: sin(3π/4) lies in the second quadrant. In second quadrant value of sin is positive.

Q: Express sin 5x cos 3x as a sum of trigonometric functions.

A: Given           sin 5x cos 3x

Q: use a calculator to solve each equation on the interval 0 ≤θ &lt; 2π. Round answers to two decimal…

A: Given: tanθ=5 To Find: find θ on the interval 0≤θ≤2π.

Q: The suitable substitution to evaluate sin24(x + 2) dx is

A: Proceed as shown below...

Q: Find the exact value of the expression: sec sin 17

A:

Q: sin 2tan

A:

Q: Use a calculator to approximate the value to four decimal places. sin 2

A:

Q: Use a calculator to find the approximate value of each expression rounded to two decimal places.;sin…

A: We have to find the value of sin1

Q: State the half-angle identities used to integrate sin x and cos x.

A: Half Angle Identities are the formulae/relationships used in trigonometric functions to reduce the…

Q: Which inverse trigonometric function has a range of 0 &lt; y &lt; π?

A: To find which inverse trigonometric function has a range of 0&lt;y&lt;π, that is the interval 0,π…

Q: Use a sketch to find the exact value of the expression sec [sin-1 (- 1/4)]

A: Let y=sec[sin-1(-1/4)]  perpendicular=-1 hypotenuse=4 base=-(-1)2+(4)2=15

Q: Find the exact value of:

A:

Q: Use a sketch to find the exact value of:

A:

Q: Use the definitions and the derivatives of sin(θ) and cos(θ) to check the derivatives of the other…

A:

Q: Evaluate the trigonometric function using its period as an aid. sin(9n)

A:

Q: Simplify sin(x−π/2) to a single trig function using a sum or difference of angles identity.

A: Given expression

Q: Determine the values of the other functions given that tanθ= 4/11, θ not included in the first…

A: Given that: tanθ=411 and θ not included in first quadrant.

Q: Why is cos(sin^-1(x)) equal to sqrt(1-x^2)?

A:

Q: Use a sketch to find the exact value of the expression sec [sin-1 (-√2/ 2)]

A: Given: secsin-1-22 we know that sin-1-12=-π4                                        ..1

Q: Which of the six trigonometric functions are undefined when  x = 0?

A:

Q: Find the derivative of sec−¹(x). Write the answer without any trigonometric functions.

A: You must have the idea of differentiation of trigonometric functions.

Q: /2 sin-1 (-)

A:

Q: Plot sin (x) and cos (x) on the same figure, then on the same axis using different colors. Where 0…

A: A graphing utility is used to plot the graph of a function.

Q: Solve the equation on the interval 0≤θ≤2π tanθ=-(sqrt)2 sinθ

A: For solving this trigonometric equation, we have to write the given equation in factored form and…

Q: Find all solutions of the equation. tan x sin x + sin x = 0

A: First, we factor the equation

Q: tan x = 2 cosx tan x

A:

Q: Use a calculator to solve the equation sin x = 0.7392 correct to four decimal places, on the…

A: GivenSinx=0.7392 interval [0,2π)

Q: Find the exact value. Show all work, including a sketch: cos(sin-1 (),

A: We have to find the exact value

Q: Find the exact value of the expression. -(들)) sec sin 13

A:

Q: Use the definitions and the derivatives of sin(θ) and cos(θ) to check the derivatives of the other…

A: Given :     f(θ) = cot(θ)

Q: Use the definitions and the derivatives of sin(θ) and cos(θ) to check the derivatives of the other…

A: We know that ddxf(x)n = n·f(x)n-1·f'(x) ddxf(x)g(x) = g(x)·f'(x)-f(x)·g'(x)g(x)2 ddθsin(θ) = cos(θ)…

Q: Find two values of θ, 0 ≤θ &lt;2π, that satisfy the equation tan tan θ = -√3.

A: Given:tanθ=-3

Q: , given tan x = -4 and cos x < 0

A: Given that tan x and cos x both have negative values , So, the value of x must lies in 2nd quadrant…

Q: Find all solutions of the equation: tan x = 1

A:

Q: Consider the equation sin 2x-ex=0.- a) By sketching two familiar functions, show that this equation…

A:

Q: Solve the equation on the interval [0,2x). cot x tan x+ 3.

A: Equation given in the question is: We can solve each part separately as follows:

Q: Can we use the same techniques to find the derivatives of the other three inverse trigonometric…

A: here we have to use the same techniques to find the derivatives of the other three inverse…

Q: Find the exact value of the expression whenever it is defined.

A: To find the exact value of the expression whenever it is defined.           cos-1sin 0

Q: To graph y = sin(-Bx) for B > 0, first write the function as y = because sine is an -Select---v…

A: Given query is to fill the blank.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.