if cosØ=0.6 and 0°<Ø<90°, find the exact value of 2Ø
remember cos^2 Ø + sin^2 Ø = 1
.36 + sin^2 Ø = 1
sin^2 Ø = .64
sinØ = .8
sin 2Ø = 2sinØcosØ
= 2(.8)(.6)
= .96
2Ø = sin^-1 (.96) or arcsin(.96)
To find the exact value of 2Ø, we need to first find the value of Ø.
Given that cosØ = 0.6 and 0° < Ø < 90°, we can apply the inverse cosine function to find the value of Ø.
So, Ø = cos^(-1)(0.6)
To find the exact value, we'll calculate it using a calculator.
Using a calculator, the inverse cosine of 0.6 is approximately 53.13°.
Now that we know the value of Ø, we can find 2Ø.
2Ø = 2 * 53.13°
Calculating this expression, 2Ø = 106.26°.
Therefore, the exact value of 2Ø is 106.26°.