Grade 9 Math: Sum and Difference Identities
This worksheet focuses on understanding and applying sum and difference identities for sine, cosine, and tangent functions.
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Standards
Topics
Sum and Difference Identities
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. The sum identity for sine is sin(A + B) = .
2. The difference identity for cosine is cos(A - B) = .
3. The sum identity for tangent is tan(A + B) = .
4. Which of the following is the correct difference identity for sine?
sin A cos B + cos A sin B
sin A cos B - cos A sin B
cos A cos B + sin A sin B
cos A cos B - sin A sin B
5. Which identity would you use to simplify sin(75°)?
Sum identity for sine
Difference identity for sine
Sum identity for cosine
Difference identity for cosine
6. Use the sum identity for sine to find the exact value of sin(105°). Show all your steps.
7. Use the difference identity for cosine to find the exact value of cos(15°). Show all your steps.
8. sin(A - B) = sin A cos B + cos A sin B
True
False
9. cos(A + B) = cos A cos B - sin A sin B
True
False
10. If sin A = 3/5 and cos B = 5/13, where A and B are acute angles, find the exact value of sin(A + B).