Question

Given that sin 2π/3= cos y, first express 2π/3 as a sum of π/2 and angle and then apply a trigonometric identity to determine the measure of angle y.

Answer 1

`y=(\pi)/(6)`

Explanation:

Given that:

`\sin((2\pi)/(3))=\cos y`

Substitute the value
`(2\pi)/(3)=(\pi)/(2)+(\pi)/(6)`.

`\sin((\pi)/(2)+(\pi)/(6))=\cos(y)`

(Using the formula:
`\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta`)

`\sin(\pi)/(2)\cos(\pi)/(6)+\cos(\pi)/(2)\sin(\pi)/(6)=\cos y`

Using
`\sin(\pi)/(2)=1, \cos(\pi)/(2)=0`, we obtain:

`1*\cos(\pi)/(6)+0* \sin(\pi)/(6)=\cos y`

This is equivalent to:

`\cos(\pi)/(6)=\cos y`

Applying cos inverse on both sides, we get:

`y=(\pi)/(6)`