Question 974070: Hi! I'm having tough time solving a certain math problem. I saw the answer on this site but the person who answered it did not explain how he/she got the one of the answers; I already have the answers on the back of my book, I just need a little enlightenment on how to get there! The problem is the following:
Given tan of theta = 4, use trigonometric identities to find the exact value of:
(a) (sec of theta)ˆ2. (b) cot of theta (c) cot of pi/2 - theta <-- this is where I'm struggling
(d) (csc of theta)ˆ2
Thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given tan of theta = 4, use trigonometric identities to find the exact value of:
Since tan = y/x, y = 4 and x = 1
Then r = sqrt[4^2+1^2] = sqrt(17)
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So, cos(t) = x/r = 1/sqrt(17)
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Your Problems:
(a) (sec of theta)ˆ2 = tan^2 + 1 = 4^2+1 = 17
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(b) cot of theta = 1/4
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(c) cot of (pi/2 - theta) <-- this is where I'm struggling
= tan(t) = 4
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(d) (csc of theta)ˆ2 = 1 + cot^2(t) = 1+(1/4)^2 = 17/16
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Cheers,
Stan H.
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Keep in mind::
sin^2 + cos^2 = 1
Divide thru by sin^2 to get 1 + cot^2 = csc^2
Divide thru by cos^2 to get tan^2 + 1 = sec^2
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