Question

Cos \theta =-(5)/(13) ∅and sin θ > 0. Identify the quadrant of θ and find sin θ.

Answer 1

Answer: D. Qufdrant: II

sinΘ=12/13

Explanation:

`\displaystyle\\cos\theta=-(5)/(13) \ \ \ \ sin\theta > 0\\\\sin^2\theta+cos^2\theta=1\\\\sin^2\theta=1-cos^2\theta\\\\sin\theta=б√(1-cos^2\theta) \\\\sin\theta > 0, \ \ hence\\\\sin\theta=√(1-cos^2\theta) \\\\sin\theta=\sqrt{1-(-(5)/(13))^2 } \\\\sin\theta=\sqrt{1-(25)/(169) } \\\\sin\theta=\sqrt{(169-25)/(169) } \\\\sin\theta=\sqrt{(144)/(169) } \\\\sin\theta=(12)/(13)`

`\displaystyle\\\left \{ {{cos\theta < 0} \atop {sin\theta > 0}} \right. \ \ \ \ \Rightarrow\ \ \ \ quadrant\ II`