Question

Given that cosθ= 5/13 and that θ lies in Quadrant IV, what is the exact value of sin 2θ? Answers:
`(120)/(169)`
`(24)/(13)` -
`(24)/(13)` -
`(120)/(169)`

Answer 1

`-(120)/(169)`

Explanation:

Given

`cos\theta=(5)/(13),-(3\pi)/(2)<\theta<2\pi\\sin(2\theta)=?`

Use identities

`sin(2\theta)=2sin\theta cos\theta\\\\sin(2\theta)=2(-(12)/(13))((5)/(13))\\ \\sin(2\theta)=2(-(60)/(169))\\ \\sin(2\theta)=-(120)/(169)`