Question

Calculate cos(480°) and sin(480°).

Answer 1

Answer:

$\cos(480^\circ)=-\dfrac{1}{2}$

$\sin(480^\circ)=\dfrac{\sqrt{3}}{2}$

Step-by-step explanation:

Calculate the value of trigonometry function.

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

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

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

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

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

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

$\Rightarrow -\dfrac{1}{2}$

Therefore, cos(480°) = -0.5

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

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

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

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

$\Rightarrow \dfrac{\sqrt{3}}{2}$

Therefore, sin(480°) = 0.866