Question

Which expression is equal to –1? cot StartFraction pi Over 4 EndFraction sin StartFraction pi over 2 EndFraction sin StartFraction 3 pi Over 2 EndFraction tan StartFraction 5 pi Over 4 EndFraction

Answer 1

C. sin 3pi/2

Explanation:

Plug all of the answers into your calculator and you find that the value for sin3pi/2 is -1 :)

Answer 2

Given:

The four expression in the options.

To find:

Which expression is equal to –1.

Solution:

In option A,

`\cot \left((\pi)/(4)\right)=1`

In option B,

`\sin \left((\pi)/(2)\right)=1`

In option C,

`\sin \left((3\pi)/(2)\right)=\sin \left(\pi+(\pi)/(2)\right)`

`\sin \left((3\pi)/(4)\right)=-\sin \left((\pi)/(2)\right)`
`[\because \sin(\pi+\theta)=-\sin \theta]`

`\sin \left((3\pi)/(4)\right)=-1`

In option D,

`\tan \left((5\pi)/(4)\right)=\tan \left(\pi+(\pi)/(4)\right)`

`\tan \left((5\pi)/(4)\right)=\tan \left((\pi)/(4)\right)`
`[\because \tan(\pi+\theta)=\tan \theta]`

`\tan \left((5\pi)/(4)\right)=1`

Therefore, the correct option is C.