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Anvisha [2.4K]
3 years ago
13

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.

Mathematics
1 answer:
Rina8888 [55]3 years ago
3 0

Answer:

θ = -33.69°

Step-by-step explanation:

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

Dividing both equations:

\frac{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!

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