More Math Problems

Question

Find the value of the other five trigonometry functions. Also find the reference angle and use it to determine the least positive value of  θ to the nearest 0.1°.

cosθ = -5/13, tanθ < 0

Answer 1

Using x instead of theta:

tan x = sin x/cos x

If cos x is negative and tan x is also negative, then sin x must be positive, which places us in quadrant II.

since cos^2 (x) + sin^2 (x) = 1, (-5/13)^2 + sin^2 (x) = 1, 25/169 + sin ^2 (x) = 1, sin^2(x) = 144/169 and sin x = 12/13 (since it is positive)

tan (x) = sin(x)/cos(x) = -12/5

cot (x) = 1/tan(x) = -5/12

sec (x) = 1/cos(x) = -13/5

csc(x) = 1/sin(x) = 13/12

the arccos(-5/13) = 112.6, the reference angle is (180-112.6) = 67.4