find an angle theta

Question

find an angle (theta) with 0 degrees < theta < 360 degrees that has the same:

Sine as 80 degrees: theta = ? degrees

Cosine as 80 degrees: theta = ? degrees

Answer 1

sin80° = sin(180° - 80°) = sin100°

cos80° = cos(360° - 80°) = cos280°

Answer 2

We have the trigonometric identity:

sin(pi-x) = sin(x)

sin(80°) = sin(180°-80°) = sin(100°)

Theta = 100°

We also have the trigonometric identity:

cos(360°-x) = cos(x)

cos(80°) = cos(360-80°) = cos(280°)

Theta = 280°