Question

Which equation shows that the Pythagorean identity is true for 0=3pi/2

Answer 1

Given that,

To find the equation which shows Pythagoras identity is true for theta=3 pi/2

The equation is of the form,

`\sin ^2((3\pi)/(2))+\cos ^2((3\pi)/(2))=1`

we have that,

`(3\pi)/(2)=\pi+(\pi)/(2)`

Using this we get,

`\begin{gathered} \sin (3\pi)/(2)=\sin (\pi+(\pi)/(2)) \\ =-\sin ((\pi)/(2)) \\ \sin (3\pi)/(2)=-1----\mleft(1\mright) \end{gathered}`
`\cos (3\pi)/(2)=\cos (\pi+(\pi)/(2))=0-----(2)`

Substitute the values in the given equation we get,

`(-1)^2+0^2=1`

Answer is: Option B:

`(-1)^2+0^2=1`