NEED HELP ASAP: given that tan(θ)=-2/3 and cos(θ)>0, find cos(θ) and csc(θ). don't use trigonometric identities.

Question

Please include a picture of the angle and labeled

Answer 1

Hi Melissa,

Since the tangent is negative and the cosine is positive according to the problem givens, then the angle must be in the second quadrant. Based on SOHCAHTOA, Tan(θ) = Opposite / Adjacent = 2/(−3) in other words opposite = 2 , Adjacent = −3 and using the Pythagorean Theorem the hypothesis = sqrt( 2^2 + (−3)^2) = sqrt(13). Now cos(θ) = Adjacent / Hypothesis = −3 / sqrt(13) and csc(θ) = 1 / sin(θ) = Hypothesis / Opposite = sqrt(13) / 2. I hope this was helpful!