How do you evaluate $sin(( 7pi) / 2)$ ?

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Answer 1 · 2018-04-15T08:52:16

$sin((7pi)/2)=-1$

We know that,

$color(red)(sin(3pi+theta)=-sintheta$

Here,

$sin((7pi)/2)=sin((6pi+pi)/2)$

$=sin(3pi+pi/2)...toIII^(rd) Quadrant, where, sin is -ve$

$=-sin(pi/2)$

$=-1$

Note:
$(1)theta=pi/2,(5pi)/2,(9pi)/2,(13pi)/2...=>sintheta=1$
$(2)theta=(3pi)/2,(7pi)/2,(11pi)/2,(15pi)/2...=>sintheta=-1$

How do you evaluate sin(( 7pi) / 2)sin(( 7pi) / 2)?