Sum and difference identities: exact values and trig equations

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Bo's ramp makes an angle A with tan A = 0.75, and a second ramp adds angle B with tan B = 0.5. What is tan(A + B)?

   2
2. 2.

   In math club, Esme has tan A = 2 and tan B = 0.25 (both angles acute). What is tan(A + B)?

   4.5
3. 3.

   Jun solves cos x cos 20° − sin x sin 20° = 0 for 0° ≤ x < 360°. What are the answers?

   • 70° and 250°
   • 90° and 270°
   • 110° and 290°
4. 4.

   Luz solves cos x cos 30° + sin x sin 30° = √3/2 for 0° ≤ x < 360°. What are the answers?

   • 30° and 330°
   • 0° and 60°
   • 60° and 300°
5. 5.

   Milo says sin(A + B) = sin A + sin B. Agree or disagree?

   • Agree: it works for A = 0°
   • Disagree: try A = B = 45°
   • Agree: the angles add, so the sines add
6. 6.

   Noah says sin 90° = sin 30° + sin 60°. Agree or disagree?

   • Disagree: the sum is over 1
   • Agree: 30° + 60° = 90°
   • Agree: both are special angles
7. 7.

   Pia says cos(A + B) = cos A cos B + sin A sin B. Agree or disagree?

   • Disagree: it has a minus
   • Agree: a sum gives a plus
   • Agree: cosine copies sine's sign
8. 8.

   Ren finds sin 105° exactly. Which is right?

   • −(√6 + √2)/4
   • (√6 + √2)/4
   • (√2 − √6)/4
9. 9.

   Tala finds cos 105° exactly. Which is right?

   • (√6 − √2)/4
   • (√6 + √2)/4
   • (√2 − √6)/4
10. 10.

    Zee finds sin 165° exactly. Which is right?

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