Graphs of sine and cosine and inverse functions
Answers are for parents and teachers.
1
State the amplitude, range and period of y = 4 sin θ.
Amplitude 4, range [−4, 4], period 2π.
2
Find sin(7π/2) and cos(5π).
sin(7π/2) = sin(3π/2) = −1; cos 5π = cos π = −1.
3
A tank has h = 0.4 sin θ m above its calm depth of 2 m. Find the depth when θ = 7π/6 and the least depth.
h = 0.4 × (−½) = −0.2, so the depth is 1.8 m; the least depth is 1.6 m.
4
Solve sin θ = −0.8 for 0° ≤ θ < 360°, to 2 decimal places.
Reference angle 53.13°, quadrants 3 and 4: θ = 233.13° or 306.87°.
5
A ramp is 4 m long and rises 1.5 m. Find its angle with the ground, to 1 decimal place.
sin θ = 1.5/4 = 0.375, θ ≈ 22.0°.