SOLUTION: You are given the value of tan θ. Is it possible to find the values of all the other trigonometric functions without finding the actual measure of the angle θ?

Question 972990: You are given the value of tan θ. Is it possible to find the values of all the other trigonometric functions without finding the actual measure of the angle θ?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Trick question. Except for cotangent, you cannot find THE value of the other functions, you can only find all possible values of the other functions.

For example, let

Then from the definition of tangent,

Square both sides

Use the Pythagorean Identity

Then do a bunch of algebra that I will let you verify on your own:

Similarly

And the other three functions are just the reciprocals of the ones we now know.

However, for any given non-zero value of

, there are two values for sine, cosine, secant, and cosecant. So, depending on exactly what your instructor meant by "...find the values of all the other trigonometric functions without finding the actual measure of the angle", the answer to your question is either yes or no.

John

My calculator said it, I believe it, that settles it

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SOLUTION: You are given the value of tan &#952;. Is it possible to find the values of all the other trigonometric functions without finding the actual measure of the angle &#952;?

SOLUTION: You are given the value of tan θ. Is it possible to find the values of all the other trigonometric functions without finding the actual measure of the angle θ?