Solve the equation on the interval 0 x < 360. Express the solution(s) rounded to one...

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LAKERS08

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...decimal place.? 2 + 13 sin x = 14 cos^2 x


a.34.9 degrees , 145.2degrees
b. 55.2 degrees , 124.9 degrees
c.34.9, 214.9 degrees
d.214.9, 325.2 degrees
 
If you have no idea how to solve it you could plug in the answers and see which ones work. You caould also look in a textbook for help.

2 + 13 sin x = 14 cos^2 x

recall that
cos^2 x = (1 - sin^2 x)

2 + 13 sin x = 14(1 - sin^2 x)

2 + 13 sin x = 14 - 14 sin^2 x

14 sin^2 x + 13 sin x -12 = 0

14 sin^2 x + 21 sin x - 8 sin x - 12 = 0

7sin x(2 sin x + 3) - 4 (2 sin x - 3)=0

(7sin x - 4)(2sin x - 3) = 0

7sin x=4
sin x =4/7
x = 34.9

or
2sin x = 3
sin x = 3/2
x = not possible

since sin x = sin (180-x)
the answers are 34.9 and 145.2
 
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