SOLUTION: 1. Find csc theta if cot theta = 0.8 when theta is in quad III. 2. Find cos2theta and sin theta/2 if tan theta=-1/2 and theta is in quad II.

Question 1041327: 1. Find csc theta if cot theta = 0.8 when theta is in quad III.
2. Find cos2theta and sin theta/2 if tan theta=-1/2 and theta is in quad II.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1. Find csc theta if cot theta = 0.8 when theta is in quad III.
cot = x/y = 4/5
r = sqrt(x^2 + y^2) = sqrt(41)
csc = r/y = -sqrt(41)/5 **** negative in Q3
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2. Find cos2theta and sin theta/2 if tan theta=-1/2 and theta is in quad II.
tan = y/x = -1/2
r = sqrt(5)
---
sin(t) = y/r = sqrt(5)/5 (+ in Q2)
cos(t) = x/r = -2sqrt(5)/5 (- in Q2)
----
cos(2t) = 2cos^2(t) - 1 = -0.2
----
sin^2(t) = (1 - cos(t))/2 = (1 + 2sqrt(5)/5)/2 = 1/2 + sqrt(5)/5 = (5 + 2sqrt(5))/10

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