Question

I need as much shown work as possible and explanation please

Answer 1

Part A:

The cosine sum identity is given below as

`\cos(A+B)=\cos A\cos B-\sin A\sin B`

For cos 240, we will have

`\begin{gathered} \cos240=cos(180+60) \\ \end{gathered}`

By applying the rule, we will have

`\begin{gathered} \cos(180+60)=\cos180\cos60-\sin180\sin60 \\ \cos(180+60)=-1((1)/(2))-0((√(3))/(2)) \\ cos240=cos(180+60)=-(1)/(2) \end{gathered}`

Hence,

The value of cos 240 is

`\Rightarrow\cos240=cos(180+60)=-(1)/(2)`

Part B:

The sine difference identity is given below as

`\sin(A-B)=\sin A\cos B-\sin B\cos A`
`\sin240=sin(360-120)`
`\begin{gathered} \sin(A-B)=\sin(A)\cos(B)-\sin(B)\cos(A) \\ sin240=sin(360-120)=sin360cos120-sin120cos360 \\ sin240=sin(360-120)=0(cos120)-1(sin120) \\ sin240=sin(360-120)=-sin120 \\ sin240=sin(360-120)=-sin(180-120) \\ sin240=sin(360-120)=-sin60 \\ sin240=sin(360-120)=-(√(3))/(2) \end{gathered}`

Hence,

The final answer of sin240 is

`\Rightarrow-(√(3))/(2)`