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Grade 12 Trigonometric Identities Worksheet

This worksheet covers fundamental trigonometric identities, including reciprocal, quotient, Pythagorean, and sum/difference identities, suitable for Grade 12 mathematics students.

Grade 12 Math TrigonometryTrigonometric Identities
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Includes

Fill in the BlanksMultiple Choice3 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSG.SRT.C.8CCSS.MATH.CONTENT.HSF.TF.C.8

Topics

TrigonometryIdentitiesHigh School MathGrade 12
8 sections · Free to use · Printable
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Trigonometric Identities Review

Name:

Date:

Score:

Read each question carefully and provide the most simplified answer. Show all your work for full credit.

1. The reciprocal identity for sine is csc θ =  .

2. The quotient identity states that tan θ =   / cos θ.

3. One of the Pythagorean identities is sin²θ + cos²θ =  .

4. Which of the following is equivalent to 1 + cot²θ?

a

sec²θ

b

csc²θ

c

tan²θ

d

sin²θ

5. Simplify the expression: (1 - sin²θ) / cos θ

6. The identity tan(A + B) = (tan A + tan B) / (1 - tan A tan B) is true for all angles A and B where the terms are defined.

T

True

F

False

7. Prove the identity: tan θ + cot θ = sec θ csc θ

8. Without using a calculator, find the exact value of cos(75°). (Hint: 75° = 45° + 30°)