Question

If sin ø = .6 and cos ø >0, find sin 2ø and cos ø/2?

Answer 1

sin 2t = 0.96
`cos (t/2) = 0.95`

Explanation:

sin t = 0.6. Find cos t.
`cos^2 t = 1 - sin^2 t = 1 - 0.36 = 0.64` --> `cos t = +- 0.8`
since cos t > 0 --> cos t = 0.8
sin 2t = 2sint.cos t = 2(0.6)(0.8) = 0.96
To find `cos (t/2)`, use the trig identity;
`2cos^2 a = 1 + cos 2a`
`2cos^2 (t/2) = 1 + cos t = 1 + 0.8 = 1.8`
`cos^2 (t/2) = 0.9`
`cos (t/2) = +- 0.95`
since cos t > 0, then, `cos (t/2) > 0`
`cos (t/2) = 0.95`