Question

If sin theta = 1/3 and tan theta is less than 0 what is the value of cosine theta

Answer 1

Draw a triangle: QUADRANT 2 since tan(θ) is less than 0.

Sides: 1, 2√2, 3 (PYTH. THEOREM)

cos(θ)= (2√2)/3

Answer 2

If sin theta is 1/3, then theta is in either QI or Q2. If tan theta is negative, then theta is in either Q2 or Q4. Thus, theta is in Q2.

If sin theta = opp / hyp = 1/3, then opp=1 and hyp=3. Thus, adj=sqrt(3^2-1^2), or sqrt 8, or 2sqrt 2.

Then cos theta = adj / hyp = 2sqrt(2) / 3.