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12345 [234]
4 years ago
7

Calculate cos(480°) and sin(480°).

Mathematics
1 answer:
hram777 [196]4 years ago
7 0

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

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