Sum and difference identities: exact values and trig equations

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari's robot turns A, with sin A = 0.6 and cos A = 0.8, then B, with cos B = 0.936 and sin B = 0.352. Find sin(A + B) to 3 decimal places.

   0.843
2. 2.

   On Bo's worksheet, sin A = 0.28, cos A = 0.96, cos B = 0.6 and sin B = 0.8. What is sin(A + B)? Round to 3 decimal places.

   0.936
3. 3.

   Esme's spinner turns A (sin A = 0.8, cos A = 0.6), then B (cos B = 0.8, sin B = 0.6). What is sin(A + B)?

   1
4. 4.

   Using the table, which two special turns make 75° for Jun?

   • 45° + 30°
   • 60° + 30°
   • 45° + 60°
5. 5.

   Which formula does Milo use for sin(A + B)?

   • sin A cos B + cos A sin B
   • sin A + sin B
   • sin A sin B + cos A cos B
6. 6.

   Which formula does Noah use for cos(A + B)?

   • cos A cos B + sin A sin B
   • cos A + cos B
   • cos A cos B − sin A sin B
7. 7.

   In Pia's formula for cos(A − B), what sign sits between the two products?

   • Plus
   • Minus
   • Times
8. 8.

   Ren wonders if sin(30° + 60°) equals sin 30° + sin 60°. Does it?

   • No: 1 is not about 1.37
   • Yes: both are about 1.37
   • Yes: both equal 1
9. 9.

   Using the formula, what is cos(45° + 45°), Tala?

   • √2
   • 1
   • 0
10. 10.

    Using the formula, what is sin(60° − 30°), Zee?

    • 0
    • √3/2 − 1/2
    • 1/2