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Find the exact value of the indicated trigonometric function of θ.

sec θ = 9/8, θ in quadrant IV Find tan θ.

 May 27, 2020
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Since  cos(X) = 1/sec(X):  cos(X)  =  8/9.

Knowing that  cos  =  x/r  --->   x = 8  and  r = 9

Since x2 + y2  =  r2   --->   82 + y2  =  92   --->   64 + y2  =  81   --->   y2  =  17

Since the angle is in the fourth quadrant, y is negative:                      y  =  - sqrt(17)

 

tan(X) = y/x  =  - sqrt(17) / 8

 May 27, 2020

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