If tan theta = 3/4 where theta lies in the 3rd quadrant then the values of sin theta + - Maths - Introduction to Trigonometry

Question

If tan theta = 3/4 where theta lies in the 3rd quadrant then the
values of sin theta + cos theta is - A 5/7, B 7/5, C -5/7, D -7/5

Manbar Singh · Accepted Answer

We have,tan θ = 34Now, sec θ = -1+tan2θ        as, sec θ is -ve in third quadrant⇒sec θ = -1 + 342⇒sec θ = -1 + 916⇒sec θ = -54Now, cos θ = 1sec θ = -45Now, sin θ = -1 - cos2θ   as, sin θ is -ve in third quadrant=-1 - 1625=-35Now, sin θ + cos θ = -35 - 45 = -75

If tan theta = 3/4. where theta lies in the 3rd quadrant then the values of sin theta + cos theta is - A.5/7, B. 7/5, C. -5/7, D. -7/5