Precalculus Math

Question

Find the coordinates of the point at  1154 degrees on a circle of radius 3.7 centered at the origin.

Find the coordinates of the point at -130 degrees on a circle of radius 3.8 centered at the origin.

(a) Find an angle θ, with 0∘<θ<360∘, that has the same cosine as 59∘ (but is not 59∘).

(b) Find an angle θ, with 0∘<θ<360∘, that has the same sine as 59∘ (but is not 59∘).

Answer 1

Going around the circle 3 times means going 3(360°) = 1080° leaving 72° from the original 1154° (1154° - 1080° = 72°).

Using trig ratios, cos(72°) = adjacent/hypotenuse = x/3.7 so x = 3.7cos(72°) ≈ 1.14 and sin(72°) = opposite/hypotenuse = y/3.7 so y = 3.7sin(72°) ≈ 3.52 so the coordinate is approx (1.14, 3.52)

For an angle of -130° on a circle of radius 3.8, the point has coordinates (x, y) of (3.8cos(-130), 3.8sin(-130)) = (-2.44, -2.91)

The same cosine means the same x-value meaning θ = -59° which is the same as 360° - 59° = 301°

The same sine means the same y-value meaning 59° up from the -x axis which 180° - 59° = 121°