Question 69642
I have been studying for an hour and cannot figure out how to do these problems. How do I find the exact value of a trigonometric funtion such as tan135 degrees? Thank you for your help.
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Draw a "unit-circle" centered at (0,0) of an xy-coordinate system.

Draw the terminal side of a 135 Degree angle.
From the point where the terminal side meets the circle, draw a perpendicular
to the negative x-axis.  That will cut of a segment of the negative x axis.
Do you see the right triangle you have just created?
The terminal side is the hypotenuse; the perpendicular line segment is a side;
the piece of the negative x axis is the third side.
This is a 45-45-90 degree right triangle because you drew a 135 degree angle
as an external angle.
But the hypotentuse is 1 because you drew a "unit-circle".
Using Pythatgoras you can show that the other two sides are each 1/sqrt2.
The coordinates of the point where the terminal side meets the circle 
are (-1/sqrt2, 1/sqrt2) 
The cosine of 135 degrees is x/r or adj/hyp
Therefore the cos135 = (-1/sqrt2)/1 = -1/sqrt2
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Cheers,
Stan H.