Signs and basic relations
Answers are for parents and teachers.
1
For α = 4π/3 determine the signs of sin α, cos α and tan α.
sin α < 0, cos α < 0, tan α > 0 (quadrant III)
2
In which quadrant does 1000° lie and what is the sign of sin 1000°?
1000° = 2 · 360° + 280°, quadrant IV; sin 1000° < 0
3
If cos α = 12/13 and 3π/2 < α < 2π, find sin α.
−5/13
4
If tan α = 3 and 0 < α < π/2, find cos α.
√10/10
5
Derive 1 + tan²α = 1 : cos²α from sin²α + cos²α = 1.
Divide both sides by cos²α: tan²α + 1 = 1 : cos²α.