Given cos q = - 1/5 and tan q> 0, find sin q

cos (q) = ⁻¹/₅

cos⁻¹[cos (q) ] = cos⁻¹ (⁻¹/₅)

q ≈ 1.54

tan (q) > 0

tan⁻¹[tan (q) ] > tan⁻¹ (0)

q > 0

tan (1.54) > 0

0.03 > 0

sin (q) = sin (1.54)

sin (q) ≈ 0.03

Since tan (1.54) is equal to sin (1.54), they are both greater than zero.