Question 507339: Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS. If the answer involves a square root it should be entered as sqrt.
If tan(theta)=4/3 and sin(theta)<0, then find:
a)sin(theta)
b)cos(theta)
c)sec(theta)
d)csc(theta)
e)cot(theta)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS. If the answer involves a square root it should be entered as sqrt.
If tan(theta)=4/3 and sin(theta)<0, then find:
----
tan(theta) = y/x = 4/3
So, y = 4 and x = 3
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Since tan is positive and sin in negative, theta is in the 3rd Quadrant
where x and y are negative.
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Find "r":
r = sqrt[3^2+4^2] = 5
--------
sin = y/r = -4/5
cos = x/r = -3/5
tan = y/x = 4/3
----
csc = r/y = -5/4
sec = r/x = -5/3
ctn = x/y = 3/4
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Cheers,
Stan H,
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a)sin(theta)
b)cos(theta)
c)sec(theta)
d)csc(theta)
e)cot(theta)
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