Find cos (x) if tan (x) = 5 and sin (x) < 0

Answer 1

if Tanx = 5, the sinx = 5cosx or sinx - 5 cosx = 0

sinx - 5cosx is equal to the following :(numbers in parenthesis are degrees)

5.1sin(x-78.69) 5.1cos(x-168.69)

5.1 sin(x+281.31) 5.1cos(x+191.31)

These must be equal to satisfy the condition.

The zeros for the sine functions are at x = 78.69, 258.69, -281.31, -101.31

The zeros of the cosine function are at x = 258.69, 438.69, -101.31, 78.69

sinx <= 0 for the angles 258.69 & -101.31.

cos (258.69) = -.196 and cos (-101.31) = -.196