Question 802599: 443Hello, I could use some help with this question. I tried using the trig formulas that I know, but had some trouble; if you could please solve and include your steps (so I can review and find me error), I would appreciate it!
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. Decimal points in answers are not allowed (I think this means they want the answer in radians). Use simplified radical form, if necessary.
Thank you for taking the time to answer my question.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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=-√(1-cos^2x)
=-√(1-(1/4)^2)
=-√(1-1/16)
=-√((16/16)-(1/16))
=-√(15/16)
sinx=-√15/4
tanx=sinx/cosx=-√15/1=-√15
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