Using double-angle identities, find the exact value of the trig function below. sin2\alpha if sin\alpha=(5)/(13), cos\alpha=(12)/(13)

Question

Using double-angle identities, find the exact value of the trig function below.

sin2
`\alpha` if sin
`\alpha`=
`(5)/(13)`, cos
`\alpha`=
`(12)/(13)`

Answer 1

sin2 if sin=, cos=

Explanation:

its the best anwser

Answer 2

sin 2α=2(sinα)(cosα)

Data:
sin α=5/13
cos α=12/13

sin 2α=2(sin α)(cos α)
sin 2α=2(5/13)(12/13)
sin 2α=120/169

Answer: sin 2α=120/169

we can check it out our answer:
sin α=5/13
α=sin⁻¹ (5/13)≈22.62º
cos α=12/13
α=cos⁻¹ (12/13)≈22.62º

2α=2(22.62º)=45.24º
2α=sin⁻¹ (120/169)=45.24º