The expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].
Given trigonometric expression is:
[tex]Cos(\frac{\pi }{2}+r )[/tex]
What is the value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex]?
The value of [tex]Cos(\frac{\pi }{2}+\theta )[/tex] is [tex]-Sin\theta[/tex] because [tex]\frac{\pi }{2} +\theta[/tex] lies in the second quadrant and the cosine function is negative in the second quadrant.
So, [tex]Cos(\frac{\pi }{2}+r )= -Sin r[/tex]
The range of sine and cosine functions is the same i.e. [-1,1].
Both the functions are periodic functions with periods 2π.
Hence, the expression that is equivalent to [tex]Cos(\frac{\pi }{2}+r )[/tex] is [tex]-Sinr[/tex].
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