Question

If 3 sin theta - 4cos theta = 0 find value of tan theta

Answer 1

Answer:

3sin θ - 4 cos θ = 0

3sin θ = 4cos θ

sin θ/cos θ = 4/3

tan θ = 4/3.

NOTE : tan θ is positive,so θ is in the 1st and 3rd quadrants.

sec^2 θ = 1 + tan^2 θ

sec^2 θ = 1 + 16/9 = 25/9

sec θ = +/- 5/3.

NOTE:

sec θ +ve,θ in the 1st & 4th quadrants.

sec θ -ve,θ in the 2nd & 3rd quadrants.