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Question 1026823: 1) Write sec t in term of tan t if the terminal point determined by t is in Quadrant II
2)find the exact values of the 6 trigonomatic functions of t givin cos t=-5/16, tan t less than0. Then find the exact value of 1+cot^2t
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) Write sec t in term of tan t if the terminal point determined by t is in Quadrant II
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sec is negative and tan is negative in QII
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sec(t) = (1/cos) = (sin/sin)(1/cos) = (1/sin)(sin/cos = csc(t)(tan(t)
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2)find the exact values of the 6 trigonomatic functions of t given cos t=-5/16, tan t less than 0.
By definition cos(t) = x/r
So x = -5 and r = 16
Then y = sqrt[16^2-5^2] = sqrt[231]
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tan(t) = y/x = -sqrt(231)/5
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Then find the exact value of 1+cot^2t
cot(t) = -5/sqrt(231)
1 + cot^2(t) = 1 + 25/231 = 256/231
Cheers,
Stan H.
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