Question 841252: If I am given this: if sin theta = x/3, find sin theta, cos theta, tan theta, sec theta, csc theta, cot theta.
Instructions are: find the values and simplify the radicals where appropriate. Assume theta is acute. This is college level trig.
I have so much given to me for information, I am lost on how to approach this. This would be early on in the learning process about these identities. I appreciate the help. This is part of a homework assignment. So having this process will help. I am kind of a thick nut when it comes to getting math.
Regards,
John Dixon
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! General comment: When you are told the value of any trip function you
are given two of the three values that determine all of the functions
because x^2 + y^2 = r^2
Knowing any two of these you can solve for the third:
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Your problem:
Since theta is acute, theta is in QI where opp and adj are positive
Since sin = opp/hyp, opp = x and hyp = 3
Then adj = sqrt[3^2-x^2]
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if sin theta = x/3, find sin theta, cos theta, tan theta, sec theta, csc theta, cot theta.
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sin = x/3
cos = adj/hyp = sqrt(9-x^2]/3
tan = opp/adj = x/sqrt(9-x^2)
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Then csc, sec, and cot are the inverse of sin, cos, tan
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Cheers,
Stan H.
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