Trig identities: Pythagorean, symmetry and periodicity, and sum and difference

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Zee's robot turns A, ending at (3/5, 4/5); a turn of B alone ends at (5/13, 12/13). Then the robot turns B more. What is sin(A + B)?

   56/65
2. 2.

   On Esme's unit circle worksheet, turn A ends at (-4/5, 3/5) and turn B ends at (12/13, -5/13). What is cos(A − B)?

   -63/65
3. 3.

   Jun's robot turns A, ending at (8/17, 15/17); a turn of B alone ends at (-3/5, 4/5). Then the robot turns B more. What is sin(A − B)?

   -77/85
4. 4.

   On Kira's unit circle worksheet, turn A ends at (-5/13, 12/13) and turn B ends at (3/5, -4/5). What is cos(A + B)?

   33/65
5. 5.

   On Luz's worksheet, sin A = 4/5 with A in Quadrant II, and sin B = 5/13 with B in Quadrant I. What is cos(A + B)?

   -56/65
6. 6.

   On Noah's worksheet, sin A = -3/5 with A in Quadrant IV, and cos B = -5/13 with B in Quadrant III. What is sin(A + B)?

   -33/65
7. 7.

   Ren solves sin x cos 30° + cos x sin 30° = 1/2 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   0, 120
8. 8.

   Tala's math book asks for every x with cos x cos 45° − sin x sin 45° = 0 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

   45, 225
9. 9.

   Zee solves sin x cos 60° − cos x sin 60° = 0 for 0° ≤ x < 360° on a worksheet, writing answers like 10, 20. What are all the solutions?

   60, 240
10. 10.

    Esme's math book asks for every x with cos x cos 30° + sin x sin 30° = 1/2 and 0° ≤ x < 360°, written like 10, 20. What are the solutions?

    90, 330