Find the exact value of the expression.

Question

cos(tan^-1(15/8))

Answer 1

Do you know the correct approach to this kind of question?

Draw a right triangle situated in the first quadrant, for which tan θ = 15/8.

Thus the hypotenuse will be 17 (this is one of the Pythagorean triples).

Note: you are being asked to get cos θ BECAUSE θ = ARCTAN 15/8.

Do you see it?

 

You can even check this on your calculator.

 

 

Answer 2

Use the triangle construction.   

Draw a right triangle with opposite side of length 15 and adjacent side of length 8.   The hypotenuse is then

sqrt( 15² + 8² ) = sqrt(289) = 17.   

The cosine is then  adjacent over hypotenuse =   8/17 .