SOLUTION: find possible values for theta between 0 less than or equal to x less than 360. 1) 2csc^2 + 15csc theta + 7 = 0. 2) 5cos^2 theta + 2sin theta

SOLUTION: find possible values for theta between 0 less than or equal to x less than 360. 1) 2csc^2 + 15csc theta + 7 = 0. 2) 5cos^2 theta + 2sin theta - 4 = 0. 3) 4sec^

Question 839021: find possible values for theta between 0 less than or equal to x less than 360. 1) 2csc^2 + 15csc theta + 7 = 0. 2) 5cos^2 theta + 2sin theta - 4 = 0. 3) 4sec^2 theta - 7 = 0. 4) -4cos theta + 7sin^2 theta = 3. 5) 9cot^4 - 25 = 0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find possible values for 0 <= t <= 360.
1) 2csc^2 + 15csc theta + 7 = 0.
Factor:
(2csc+1)(csc+7) = 0
csc = -1/2 or csc = -7
Note: csc(t) = -1/2 is extraneous
csc(t) = -7 implies t = 351.7868 or t = 180+8.2132 = 188.2132 degrees
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2) 5cos^2 (t) + 2sin (t) - 4 = 0
cos = [-2+-sqrt(4-4*5*-4)]/10
cos = 0.7165 or cos = -1.1165
Note: cos = -1.1165 is extraneous
----
cos(t) = 0.7165 implies t = 44.23 degrees of t = -44.23
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Cheers,
Stan H.

3) 4sec^2 theta - 7 = 0. 4) -4cos theta + 7sin^2 theta = 3. 5) 9cot^4 - 25 = 0

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