Question

Calculate cos(480°) and sin(480°).

Answer 1

`\cos(480^\circ)=-(1)/(2)`

`\sin(480^\circ)=(√(3))/(2)`

Explanation:

Calculate the value of trigonometry function.

`\cos(480^\circ)` and
`\sin(480^\circ)`

Split the angle between 0 to 90° using trigonometry formula.

`\Rightarrow \cos(360^\circ+120^\circ)`

`\Rightarrow \cos(120^\circ)`
`\because \cos(360+\theta)=\cos\theta`

`\Rightarrow \cos(180^\circ-60^\circ)`
`\because 120=180-60`

`\Rightarrow -\cos(60^\circ)`
`\because \cos(180-\theta)=-\cos\theta`

`\Rightarrow -(1)/(2)`

Therefore, cos(480°) = -0.5

`\Rightarrow \sin(360^\circ+120^\circ)`

`\Rightarrow \sin(120^\circ)`
`\because \sin(360+\theta)=\sin\theta`

`\Rightarrow \sin(180^\circ-60^\circ)`
`\because 120=180-60`

`\Rightarrow \sin(60^\circ)`
`\because \sin(180-\theta)=\sin\theta`

`\Rightarrow (√(3))/(2)`

Therefore, sin(480°) = 0.866