Trig identities: Pythagorean, symmetry and periodicity, and sum and difference
Grade 11 Math Worksheet
Circle the best answer, or write your answer on the line.
On Ren's unit circle worksheet, θ is in Quadrant IV and sin θ = -7/25. What is cos θ?
On Zee's unit circle worksheet, θ is in Quadrant II and sin θ = 11/61. What is tan θ?
Esme's robot ends a turn θ in Quadrant III with cos θ = -33/65. What is tan θ?
Jun writes sin 75° = sin(45° + 30°) = sin 45° cos 30° + cos 45° sin 30° on a worksheet. Which is the exact value of sin 75°?
- (√2 + 1)/2
- (√6 + √2)/4
- (√6 − √2)/4
- √2/2
Kira writes cos 15° = cos(45° − 30°) = cos 45° cos 30° + sin 45° sin 30° from a math book. Which is the exact value of cos 15°?
- (√6 − √2)/4
- (√2 − √3)/2
- (√6 + √2)/4
- √2/2
Luz writes sin 15° = sin(45° − 30°) = sin 45° cos 30° − cos 45° sin 30° on a worksheet. Which is the exact value of sin 15°?
- (√6 − √2)/4
- (√6 + √2)/4
- (√2 − 1)/2
- √2/2
Milo writes cos 75° = cos(45° + 30°) = cos 45° cos 30° − sin 45° sin 30° from a math book. Which is the exact value of cos 75°?
- (√6 + √2)/4
- (√3 + √2)/2
- (√6 − √2)/4
- √2/2
On Noah's unit circle worksheet, the turn θ ends at (12/13, -5/13). What is sin(-θ) + cos(-θ)?
On Ren's unit circle worksheet, the turn θ ends at (-24/25, -7/25). What is cos(-θ) − sin(-θ)?
Tala's robot ends a turn θ at (9/41, 40/41) on a unit circle floor grid. What is sin(θ + 2π) + cos(-θ)?