Question

Given that tan theta = -9/4, where 270° ≤ theta ≤ 360° a)state the 5 trigonometric ratios as a fraction b) determine the value of theta to the nearest degree

Answer 1

Explanation:

θ lies in 4th quadrant.

cos θ and sec θ are positive all other trigonometric ratios are negative.

sin θ/cos θ=-9/4

sin θ=-9/4 cos θ

we know sin² θ +cos ² θ =1

(-9/4 cos θ)²+cos ² θ =1

cos ² θ (81/16+1)=1

cos ²θ((81+16)/16)=1

cos² θ=16/97

cos θ=4/√97

sin θ=-9/4*4/√97=-9/√97

sec θ=1/cos θ=√97/4

cosec θ=1/sin θ=-√97/9

cot θ=1/tan θ=-4/9

`\ theta=tan^(-1)(-9/4) \approx 294 ^\circ`