## Trigonometric Functions Questions and Answers

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Given \sin \theta = \frac{5}{2} \text{ and } 0 \theta \frac{\pi}{2}. Find \cos \frac{\theta}{2}

Find tan(x/2) from the given information.
cos(x)= -24/25, 180 < x < 270

Given 2\cos 3\theta= 1, find the solutions in the interval [0, 2\pi).

Given 2\cos 3\theta= 1, find all solutions of the equation.

Two sides of a triangle each measure 4 mm. The angle between these two sides has a measure of 50^\circ. What is the length of the third side of the triangle?

Simplify (\sec^2\theta - 1)(\csc^2\theta\cos^2\theta).

Find the period y = -3 \tan \left (2x - \left ( \frac{\pi}{3}\right ) \right )

Find the period of the function y= 5 \tan 2x

Find the period y = tan(2x - pi/2). Graph the function.

Find the period y= 9 \tan \left( x - \frac {\pi}{4} \right)

Find the period y= \frac{1}{2} \sec x

Find the period y= 4 \cot x

Find the period y= 12 \tan x

The graph of a sine function with a positive coefficient is shown in the figure below. a. Find the amplitude, period and phase shift. b. Write the equation in the form y=a \sin (bx-c) for a0,b0, and the least positive real number c.

Let f(\theta)= 2\sin(\theta) - 1 and let g(\theta)= \frac{1}{2}\cos(\theta) + \frac{3}{2}. What is the midline and amplitude of g?

The graph of a sine function with a positive coefficient is shown below. a. Find the amplitude, period and phase shift. b. Write the equation in the form y=a \sin (bx-c) for a0,b0, and the least positive real number c.

Calculate \cos \theta\ and\ \sin \theta\ for\ \theta= 150^\circ. Leave your answer in exact form.

Express the length of x in terms of the trigonometric rations of \theta.

Solve the triangle:

Solve the equation on the interval \parenthesis 0,2\pi \parenthesis. 12\cos^{2}x = 9

Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed. \tan Z

Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed. \cos Z.

The length of the hypotenuse of a 30^\circ - 60^\circ - 90^\circ triangle is 18. What is the perimeter of the triangle?

If \sin \theta= 4/5 in quadrant II, what is \cos \theta?

If \sin \theta= \frac{5}{13} and \theta lies in quadrant III, find \cos \theta.

Find the value of \tan \theta\ for\ \cot \theta= -9 with the constraint \cos \theta greater than 0.

Verify the following identity: (tan x)/(1 - cot x) + (cot x)/(1 - tan x) = 1 + sec x csc x.

Find the exact value of cos(2arccos(7/25)). Write cos(2arccos(a/c)) as an algebraic expression in a and c for positive a and c.

Given that \sin(\theta)= 1/8 for an angle \theta in Quadrant II, find the exact value of \cos(2\theta).

Given that \sin(\theta)= 1/8 for an angle \theta in Quadrant II, find the exact value of \cos(\theta).

Suppose that \theta is an angle in a standard position whose terminal side intersects the unit circle at (-\frac{\sqrt{3}}{2}, \frac{1}{2}). Find the exact value of \cos\theta.

Suppose that \theta is an angle in a standard position whose terminal side intersects the unit circle at (-\frac{\sqrt{3}}{2}, \frac{1}{2}). Find the exact value of \sec\theta.

Suppose that \theta is an angle in a standard position whose terminal side intersects the unit circle at (-\frac{\sqrt{3}}{2}, \frac{1}{2}). Find the exact value of \cot\theta.

Suppose that \theta is an angle in a standard position whose terminal side intersects the unit circle at (-\frac{3}{5}, \frac{4}{5}). Find the exact value of \sin\theta.

Suppose that \theta is an angle in a standard position whose terminal side intersects the unit circle at (-\frac{3}{5}, \frac{4}{5}). Find the exact value of \tan\theta.

The note 'G' below the note 'middle C' is a sound wave with ordinary frequency f = 196 Hertz = 196 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and the phase shift is 0.

Find \tan 2x from the given information. \csc x= 4, \tan x less than 0.

Find \sin 2x from the given information. \csc x= 4, \tan x less than 0.

Given y=5 \sin(6x-\pi), state the period and phase shift.

Find the value of csc(theta) with the angle in a standard position and whose terminal side passes through the point (3,3).

Which of the functions corresponds to the graph? a. f(x)= \cos (2x)+2 b. f(x)= \sin x+3 c. f(x)= 2 \cos x+1 d. f(x)=3- \sin x

If \tan\theta= \frac{1}{5}, what is \cot\theta?

Find the exact value of \sin\frac{\pi}{6}.

Find the exact value of \cos\frac{3\pi}{4}.

An angle \theta has \sin \theta= \frac{35}{37} and terminal side in the second quadrant. Find the exact value of \tan \theta.

An angle \theta has \sin \theta= \frac{35}{37} and terminal side in the second quadrant. Find the exact value of \cos \theta.

Factor the expression and simplify it. 2/7 - 4/7\sin^2(x) + 2/7\sin^4(x)

Point p(2, 5) is on the terminal side of the angle \theta in standard position. Find \cot\theta.

Point p(2, 5) is on the terminal side of the angle \theta in standard position. Find \csc\theta.

Point p(2, 5) is on the terminal side of the angle \theta in standard position. Find \tan\theta.

Point p(2, 5) is on the terminal side of the angle \theta in standard position. Find \cos\theta.

Point p(2, 5) is on the terminal side of the angle \theta in standard position. Find \sin\theta.

Find the exact value without using a calculator. \sec 45^\circ

Simplify \cot\theta\ \sec\theta.

The terminal side of the angle \theta in standard position lies on the line 6x + 5y= 0 in Quadrant IV. Find \tan\theta.

The terminal side of the angle \theta in standard position lies on the line 6x + 5y= 0 in Quadrant IV. Find \cos\theta.

Find the exact value of \cos(5\pi/2) using the sum and difference identities.

For 0 less than \theta less than \pi/2, find \csc(\theta) if \tan(\theta)= 5\6.

For 0 less than \theta less than \pi/2, find \sec(\theta) if \tan(\theta)= 5\6.

For 0 less than \theta less than \pi/2, find \cos(\theta) if \tan(\theta)= 5\6.