Sum and difference identities: exact values and trig equations

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   On Ari's worksheet, cos A = 0.6, sin A = 0.8, cos B = 0.28 and sin B = 0.96. What is cos(A − B)?

   0.936
2. 2.

   Bo's robot turns A (cos A = 0.6, sin A = 0.8) and B (cos B = 0.8, sin B = 0.6). What is cos(A − B)?

   0.96
3. 3.

   In math club, Esme has cos A = 0.8, sin A = 0.6, cos B = 0.936 and sin B = 0.352. What is cos(A − B)?

   0.96
4. 4.

   Kira finds cos 15° = cos(45° − 30°) exactly. Which is right?

   • (√6 + √2)/4
   • (√6 − √2)/4
   • √3/2 − √2/2
5. 5.

   Luz finds cos 75° exactly. Which is right?

   • (√6 − √2)/4
   • (√6 + √2)/4
   • (√2 − √6)/4
6. 6.

   Noah finds tan 75° exactly. Which is right?

   • 1 + √3
   • 2 − √3
   • 2 + √3
7. 7.

   Pia tries tan(45° + 45°) with the formula. What happens?

   • The bottom is 0, so no value
   • It equals 1, like tan 45°
   • It equals 2, the sum of the tangents
8. 8.

   Ren solves sin x cos 30° + cos x sin 30° = 1 for 0° ≤ x < 360°. What is x?

   • 120°
   • 90°
   • 60°
9. 9.

   Tala solves cos x cos 10° + sin x sin 10° = 1 for 0° ≤ x < 360°. What is x?

   • 0°
   • 80°
   • 10°
10. 10.

    Which single expression matches Zee's sin x cos 50° − cos x sin 50°?

    • cos(x − 50°)
    • sin(x + 50°)
    • sin(x − 50°)