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
5. 4.

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

   • 45° + 60°
   • 60° + 30°
   • 45° + 30°
6. 5.

   Using the table, what is sin 45° × cos 30°, Kira?

   Use the picture in question 4.

   • √5/4
   • √6/2
   • √6/4
7. 6.

   Using the table, how can Luz write 15° with two special turns?

   Use the picture in question 4.

   • 60° − 30°
   • 30° − 15°
   • 45° − 30°
8. 7.

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

   • sin A cos B + cos A sin B
   • sin A sin B + cos A cos B
   • sin A + sin B
9. 8.

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

   • cos A + cos B
   • cos A cos B + sin A sin B
   • cos A cos B − sin A sin B
10. 9.

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

    • Yes: both are about 1.37
    • Yes: both equal 1
    • No: 1 is not about 1.37
11. 10.

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

    • 1/2
    • √3/2 − 1/2
    • 0