SOLUTION: How would I go about solving this. Suppose csct = 4 and tan > 0. FInd the exact value of each of the following a. sin(t-6π) b. cot(5π-t) c. cos(-t) d. sin(2t) e.

Algebra ->  Trigonometry-basics -> SOLUTION: How would I go about solving this. Suppose csct = 4 and tan > 0. FInd the exact value of each of the following a. sin(t-6π) b. cot(5π-t) c. cos(-t) d. sin(2t) e.       Log On


   

Question 922219: How would I go about solving this.
Suppose csct = 4 and tan > 0. FInd the exact value of each of the following
a. sin(t-6π)
b. cot(5π-t)
c. cos(-t)
d. sin(2t)
e. cos (t+5π/3)
I know the opp = √17 adj = 1 and hyp = 4 but how do I apply those in order to solve these?
Thank you
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How would I go about solving this.
Suppose csct = 4 and tan > 0. FInd the exact value of each of the following
Since csc positive and tan is positive, the angle is in QI
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By defition csc = r/y
Since csc = 4, 4 = 4 and y = 1
The x = sqrt[4^2-1^] = sqrt(15)
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a. sin(t-6π) = sin(t) = y/r = 1/4
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b. cot(5π-t) = cot(pi - t) = tan(t) = y/x = 1/sqrt(15)
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c. cos(-t) = cos(t) = x/r = sqrt(15)/4
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d. sin(2t) = sin^2(t)-cos^2(t) = (1/4)^2 - (sqrt(15)/4))^2 = (1-15)/16 = -14/16
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e. cos (t+5π/3) = cos(t-pi/3) = cos(t)cos(-pi/3)+sin(t)(sin(-pi/3))
= (sqrt(15)/4)(1/2) + (1/4)(-sqrt(3)/2)
= [sqrt(15)/8] - [sqrt(3)/8]
= [sqrt(15)-sqrt(3)]/8
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Cheers,
Stan H.
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I know the opp = √17 adj = 1 and hyp = 4 but how do I apply those in order to solve these?