Question 802599
If theta is a fourth-quadrant angle such that sec theta=4, use a trigonometric identity to find the exact value of the tan of theta.
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use x for theta
In quadrant IV, sin<0, cos>0, tan<0
cosx=1/secx
cosx=1/4
sinx=-&#8730;(1-cos^2x)
=-&#8730;(1-(1/4)^2)
=-&#8730;(1-1/16)
=-&#8730;((16/16)-(1/16))
=-&#8730;(15/16)
sinx=-&#8730;15/4
tanx=sinx/cosx=-&#8730;15/1=-&#8730;15