Answer:
[tex]\cos(480^\circ)=-\dfrac{1}{2}[/tex]
[tex]\sin(480^\circ)=\dfrac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Calculate the value of trigonometry function.
[tex]\cos(480^\circ)[/tex] and [tex]\sin(480^\circ)[/tex]
Split the angle between 0 to 90° using trigonometry formula.
[tex]\Rightarrow \cos(360^\circ+120^\circ)[/tex]
[tex]\Rightarrow \cos(120^\circ)[/tex] [tex]\because \cos(360+\theta)=\cos\theta[/tex]
[tex]\Rightarrow \cos(180^\circ-60^\circ)[/tex] [tex]\because 120=180-60[/tex]
[tex]\Rightarrow -\cos(60^\circ)[/tex] [tex]\because \cos(180-\theta)=-\cos\theta[/tex]
[tex]\Rightarrow -\dfrac{1}{2}[/tex]
Therefore, cos(480°) = -0.5
[tex]\Rightarrow \sin(360^\circ+120^\circ)[/tex]
[tex]\Rightarrow \sin(120^\circ)[/tex] [tex]\because \sin(360+\theta)=\sin\theta[/tex]
[tex]\Rightarrow \sin(180^\circ-60^\circ)[/tex] [tex]\because 120=180-60[/tex]
[tex]\Rightarrow \sin(60^\circ)[/tex] [tex]\because \sin(180-\theta)=\sin\theta[/tex]
[tex]\Rightarrow \dfrac{\sqrt{3}}{2}[/tex]
Therefore, sin(480°) = 0.866
