what is cos x?

Question

If 0≤x≤90 and tan x=15/8, then cos x=?

Answer 1

1 + tan²x = sec²x

 

Now sec = 1/cos, so we can rewrite the above equation as:

 

1 + tan²x = 1/cos² x

 

1 + (15/8)² = 1/cos²x

 

Solve for cos x

Answer 2

Remember the Pythagorean triple 8, 15, 17?

The reference triangle has horizontal leg 8, vertical leg 15,  hypotenuse 17...so cos x = 8/17.

 

Another way to do this is to recall that 1 + tan²x = sec²x & secant is reciprocal of cosine.