Answer:
Step-by-step 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
[tex]\ theta=tan^{-1}(-9/4) \approx 294 ^\circ[/tex]
