How do you find the exact value for sin((3pi)/2)tan(pi/4) - cos((2pi)/3)?

1 Answer
Tony B
Feb 15, 2016

-0.5

Explanation:

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A diagram Usually helps understanding

sin(pi/4) = 1/sqrt(2)

cos(pi/4)= 1/sqrt(2)

So" "color(brown)( tan(pi/4)=sin(pi/4)/cos(pi/4) = sqrt(2)/(sqrt(2) )=1)

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color(brown)(sin(3/2 pi) = -sin(pi/2)=-1 ....Corrected

Given that the hypotenuse is of constant length:
As theta increases the hypotenuse gets steeper and steeper
dragging the opposite with it. In other words the opposite gets closer and closer to the point where you are measuring the angle.
This continues until you reach pi/2 at which point the hypotenuse and the opposite coincide. Thus they are both of the same length. So sin(pi/2)=1

However, in the quadrant of pi/2 " the " y" value is negative

So sin(3/2 pi)=-1

color(brown)(sin (3/2 pi)= -1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

color(brown)(cos(2/3 pi) =-cos(1/3 pi) = -0.5

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Given:" "sin(3/2 pi)tan(pi/4)-cos(2/3 pi)

color(blue)((-1)(1) -(-0.5) = - 0.5)

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