Find the exact value c sin3pi4 d cos11pi4 e Tanpi4 Soluti

Find the exact value c) sin(3pi/4) = d) cos(11pi/4) = e) Tan(pi/4) =

Solution

What i am baout to explain is the best way to find trig values at any standard angle. It does not rely on mugging up the entire unit circle, for one :)

Here we go....

sin(3pi/4) :

3pi/4 is in quad2
So, refangle = pi - 2nd quad angle ---> formula
refangle = pi - 3pi/4 = pi/4

We know sin(pi/4) = sqrt(2)/2

And sin being positive in quadrant 2 from CAST rule,
the answer will remain

sqrt(2)/2 ---> ANSWER

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cos(11pi/4)

11pi/4 is an angle more than 2pi
So, subtract 2pi...

11pi/4 - 2pi to get 3pi/4

cos(3pi/4)

3pi/4 is in 2nd quad

Refangle = pi - 3pi/4 = pi/4

cos(pi/4) = sqrt(2)/2

And since cos is negative in quadrant 2,
final ans is

-sqrt(2)/2 ---> ANSWER

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e)
tan(pi/4)

We know that sin(pi/4) = sqr(2)/2
and cos(pi/4) = sqrt(2)/2

And knowing that tan = sin/cos,
we have

tan(pi/4) = 1 ----> ANSWER