Given:
The four expression in the options.
To find:
Which expression is equal to –1.
Solution:
In option A,
[tex]\cot \left(\dfrac{\pi}{4}\right)=1[/tex]
In option B,
[tex]\sin \left(\dfrac{\pi}{2}\right)=1[/tex]
In option C,
[tex]\sin \left(\dfrac{3\pi}{2}\right)=\sin \left(\pi+\dfrac{\pi}{2}\right)[/tex]
[tex]\sin \left(\dfrac{3\pi}{4}\right)=-\sin \left(\dfrac{\pi}{2}\right)[/tex] [tex][\because \sin(\pi+\theta)=-\sin \theta][/tex]
[tex]\sin \left(\dfrac{3\pi}{4}\right)=-1[/tex]
In option D,
[tex]\tan \left(\dfrac{5\pi}{4}\right)=\tan \left(\pi+\dfrac{\pi}{4}\right)[/tex]
[tex]\tan \left(\dfrac{5\pi}{4}\right)=\tan \left(\dfrac{\pi}{4}\right)[/tex] [tex][\because \tan(\pi+\theta)=\tan \theta][/tex]
[tex]\tan \left(\dfrac{5\pi}{4}\right)=1[/tex]
Therefore, the correct option is C.
Answer:
C. sin 3pi/2
Step-by-step explanation:
Plug all of the answers into your calculator and you find that the value for sin3pi/2 is -1 :)
