The unit circle and the six functions
Answers are for parents and teachers.
1
The terminal side passes through (−8, 15). Find sin θ, cos θ and tan θ.
r = 17: sin 15/17, cos −8/17, tan −15/8.
2
sin θ = −5/13 and θ is in the third quadrant. Find cos θ and tan θ.
x = −12: cos θ = −12/13, tan θ = 5/12.
3
Evaluate sin²60° + cos²30° − tan 45°.
(√3/2)² + (√3/2)² − 1 = ¾ + ¾ − 1 = ½.
4
Evaluate 3 tan 30° × tan 60° − 2 cos 60°.
3 × (√3/3 × √3) − 2 × ½ = 3 − 1 = 2.
5
In which quadrant is θ if tan θ < 0 and cos θ < 0?
tan θ < 0 means quadrant 2 or 4; cos θ < 0 means 2 or 3. So the second quadrant.