Defining the Unit Circle: Videos & 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

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.

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.

$\sin {39}^{\circ }$

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°