Question

If sin phi sin theta = 0.2 and sin phi cos theta = -0.3 and sin phi > 0 what is theta ? Repeat for sin phi < 0.

Answer 1

θ = -33.69°

Explanation:

For Φ>0 and Φ<0 (in general Φ≠nπ where n is an integer), sin(Φ) ≠ 0

Dividing both equations:

`(sin(\phi) sin(\theta))/(sin(\phi)cos(\theta)) = tan(\theta) = 0.2/(-0.3)=-2/3\\`

Therefore:

arctan(θ) = -2/3

θ = -33.69°

The answer does not depend on the sign of Φ, in fact we just need that the sine does not become zero, which occurs when Φ is equal to an integer times π (radians) or 180 (degrees)

Have a nice day!