Question

give the exact answers do not use decimal numbers the answer should be a fraction or an atithmetic expression

Answer 1

We are given

To find cos(2t)

`\begin{gathered} cos2t=2cos^2t-1 \\ \\ cos2t=2(-(3)/(4))^2-1 \\ \\ cos2t=2((9)/(16))-1 \\ \\ cos2t=(9)/(8)-1 \\ \\ cos2t=(1)/(8) \end{gathered}`

To find sin(2t)

`\begin{gathered} sin2t=2sintcost \\ \\ sin2t=2(-(√(7))/(4))(-(3)/(4)) \\ \\ sin2t=(3√(7))/(8) \end{gathered}`

To find cos(t/2)

`\begin{gathered} cos(t)=2cos^2((t)/(2))-1 \\ \\ cos(t)+1=2cos^2((t)/(2)) \\ \\ -(3)/(4)+1=2cos^2((t)/(2)) \\ \\ (1)/(4)=2cos^2((t)/(2)) \\ \\ (1)/(8)=cos^2((t)/(2)) \\ \\ cos^2((t)/(2))=(1)/(8) \\ \\ cos((t)/(2))=-(1)/(2√(2)) \\ \\ cos((t)/(2))=-(√(2))/(4) \end{gathered}`

To find sin(t/2)