Defining the Unit Circle Practice Problems

Determine the exact value of the given function.

sin (11π/6)

Determine the exact value of the given function.

tan (7π/4)

Determine the exact value of the given function.

csc (7π/6)

An acute angle α and trigonometric functions sin α and cos α are given. Find the remaining trigonometric functions tan α, cot α, sec α, and csc α, by using identities.

sin α = 5/13, cos α = 12/13

An acute angle α and trigonometric functions sin α and cos α are given. Find the remaining trigonometric functions tan α, cot α, sec α, and csc α, by using identities.

sin α = 6/11, cos α = (√85)/11

The trigonometric function sin α is given. Find the value of cos α by using an appropriate Pythagorean identity. Note that α is an acute angle.

sin α = 4/17

The trigonometric function sin α is given. Find the value of cos α by using an appropriate Pythagorean identity. Note that α is an acute angle.

sin α = (√65)/9

Without using a calculator, determine the value of the following trigonometric expression:

(sin 22.3°)(csc 22.3°)

Without using a calculator, determine the value of the following trigonometric expression:

[sin (π/21)] ² + [cos (π/21)] ²

Without using a calculator, determine the value of the following trigonometric expression:

-tan² 57.1° + sec² 57.1°

Which of the following cofunctions has the same value as sin 11.5°?

Which of the following cofunctions has the same value as csc 39.4°?

Which of the following cofunctions has the same value as tan (3π/13)?

Which of the following cofunctions has the same value as cos (5π/17)?

Which of the following cofunctions has the same value as sin 13.9°?

Given the following conditions, evaluate the other trigonometric functions of D.

cos D = 4/9, sin D < 0

A line passes through (6,0). This line also forms a 45° angle with the +x-axis. Determine the equation of this line in slope-intercept form.

Identify the acute angle formed between the line defined by y = ((√3)/3)x and the x-axis.

The figure consists of two adjacent right triangles. Determine the exact values of w, x, y, and z.

The figure consists of two adjacent right triangles. Determine the exact values of r, s, t, and u.

The following figure shows a 30°-60°-90° triangle. Write a formula for its area, A, in terms of m.

The following figure shows an equiangular triangle. Write a formula for its area, A, in terms of q.

The following figure shows a right triangle. Determine the values of the six trigonometric functions for angle N. Provide exact values and simplify your answers.

Determine one solution for the following trigonometric equation considering only acute angles for the trigonometric functions.

cos ((2θ/7) + 22°) = sin ((5θ/3) + 27°)

For the given triangle, determine the exact value of sin α, cos α, and tan α.

For the given triangle, determine an expression for sin α, cos α, and tan α.

Determine the missing side in the given triangle using the Pythagorean Theorem. Also, write the value of the six trigonometric ratios for angle P.

p = 9, r = 40

Determine the missing side in the given triangle using the Pythagorean Theorem. Also, write the value of the six trigonometric ratios for angle P.

p = 12, q = 37

Determine the missing side in the given triangle using the Pythagorean Theorem. Also, write the value of the six trigonometric ratios for angle P.

r = 5, q =12

Determine the missing side in the given triangle using the Pythagorean Theorem. Also, write the value of the six trigonometric ratios for angle P.

p = √7, q = 7

Which of the following is the exact value of the given trigonometric function?

tan 30°

Which of the following is the exact value of the given trigonometric function?

csc 45°

For the following trigonometric function, write it in terms of its cofunction.

sin 39°

For the following trigonometric function, write it in terms of its cofunction.

tan 47.8°

For the following trigonometric function, write it in terms of its cofunction.

cos(α + 31°)

Identify if the given statement is true or false. Provide a justification if it is false.

csc 34° ≤ csc 56°

Solve the following trigonometric equation. Consider all the angles as acute angles.

tan α = cot (α + 23°)

Solve the following trigonometric equation. Consider all the angles as acute angles.

sin(5α + 18°) = cos(4α - 27°)

Solve the following trigonometric equation. Consider all the angles as acute angles.

cot(7α + 8°) = tan(4α + 5°)

Solve the following trigonometric equation. Consider all the angles as acute angles.

cos(8α + 87°) = sin(5α - 49°)

Solve the following trigonometric equation. Consider all the angles as acute angles.

sec(5α + 14°) = csc(α + 40°)

Solve the following trigonometric equation. Consider all the angles as acute angles.

csc(α + 75°) = sec(α - 35°)

Identify if the given statement is true or false.

tan 66° ≤ tan 80°

Identify if the given statement is true or false.

cos 47° < sin 47°

Identify if the given statement is true or false.

cot 58° < tan 69°

Identify if the given statement is true or false.

csc 67° < csc 88°

Determine the exact value of the given trigonometric function.

tan 60°

Determine the exact value of the given trigonometric function.

sin 45°

Determine the exact value of the given trigonometric function.

cos 60°

Determine the exact value of the given trigonometric function.

sec 30°

Determine the exact value of the given trigonometric function.

cot 30°

Determine the exact value of the given trigonometric function.

csc 30°

Graph the following function. Consider only one period.

$y=-\frac14\csc\left(x+\frac32\pi\right)$

Identify if the given statement is true or false. Provide a justification if it is false.

tan 72° ≥ cot 27°