Unit 13 Review - Trig Identities

Simplify. 
cos²x + sin²x =

• 1

• -1

• tan²x

• π²

Answer explanation

Using the Pythagorean identity, we know that cos²x + sin²x = 1 for any angle x. Therefore, the simplified result is 1, which corresponds to the correct answer choice.

tan²x = 

• 1 + cot²x

• 1  - sec²x

• csc²x - 1

• sec²x - 1

Answer explanation

Using the identity tan²x = sec²x - 1, we can see that the correct answer is sec²x - 1. This shows the relationship between tangent and secant functions in trigonometry.

1 + cot² x = 

• csc² x

• sec² x

• sin² x

• cos² x

Answer explanation

Using the identity 1 + cot²x = csc²x, we can see that the left side simplifies to csc²x. Therefore, the correct answer is csc²x.

Simplify.
cos² x /sin² x

• tan²x

• cot²x

• sec²x

• csc²x

Answer explanation

To simplify \( \frac{\cos^2 x}{\sin^2 x} \), we can use the identity \( \cot^2 x = \frac{\cos^2 x}{\sin^2 x} \). Thus, the expression simplifies to \( \cot^2 x \), making the correct answer \( \cot^2 x \).

Simplify the trig expression.

• sinx

• cosx

• cotx

• tanx

Answer explanation

To simplify the expression, recall that tan(x) = sin(x)/cos(x). If the expression simplifies to this ratio, the correct choice is tanx.

Simplify the trig expression.

• tan²x

• 2

• cot²x

• 1

Answer explanation

To simplify the expression, recall that tan²x = sin²x/cos²x. Using the Pythagorean identity, we find that tan²x is the correct simplification, confirming that the answer is tan²x.

Please select the correct solution

• csc x

• sec x

• cot x

• tan x

Answer explanation

The correct answer is tan x because it represents the ratio of the opposite side to the adjacent side in a right triangle, which is fundamental in trigonometry. The other options represent different trigonometric functions.

• Who knows ... I have missed so many lessons.

Answer explanation

According to the even/odd identities in trigonometry, cos(-y) = cos(y). Therefore, the correct answer is cos(y).

Tags

CCSS.HSF.TF.A.2

Answer explanation

The cofunction identity states that \( \cos\left(\frac{\pi}{2}-\theta\right) = \sin(\theta) \). This means the cosine of an angle is equal to the sine of its complement, making \( \sin(\theta) \) the correct choice.

Answer explanation

The cofunction identity states that \( \sin\left(\frac{\pi}{2}-\theta\right) = \cos(\theta) \). This means the sine of an angle's complement equals the cosine of the angle, making \( \cos(\theta) \) the correct choice.