Posted by **Jason** on Wednesday, March 27, 2013 at 11:54pm.

Given \tan \theta = -\frac{4}{3}, where \frac{\pi}{2} < \theta < \pi, what is the value of \frac{1}{\sin \theta + \cos \theta}?

- Trigonometry -
**Reiny**, Thursday, March 28, 2013 at 12:01am
I will guess that you meant:

tanŲ = 4/3, π/2 < Ų < π , or Ų is in quadrant II

construct the right-angled triangle, and you should recognize the 3-4-5 triangle.

guessing that you want:

1/sinŲ + cosŲ

in II, the sine is + , but the cosine is -

sinŲ = 4/5 and cosŲ = -3/5

1/sinŲ + cosŲ

= 1/(4/5) + (-3/5)

= 5/4 - 3/5

= 13/20

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