SOLUTION: I need to evaluate the (1) sine, (2) cosine, and/or (3) tangent of the angle without using a calculator. I also need to give an EXACT answer. tan pi/2 pi/2 is a "special

Question 1092730: I need to evaluate the (1) sine, (2) cosine, and/or (3) tangent of the angle without using a calculator. I also need to give an EXACT answer.
tan pi/2

pi/2 is a "special angle" and I need to use trig properties to find the tangent but I am stuck on this one for some reason. Thanks.
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For or degrees,

So then

So is undefined.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
pi/2 is the angle in radians.
the angle in degrees would be pi/2 * 180 / pi which is equal to 180/2 which is equal to 90 degrees.

your special angle is 90 degrees.

if you tried to draw an angle of 90 degrees on a graph where the origin of the graph is the vertex of the angle, then you would find that the length of the vertical side of the triangle formed would be equal to the length of the hypotenuse and the length of the horizontal side formed would be equal to 0.

here's a neat interactive graph of an angle on the unit circles with the triangle formed that shows you what happens as the angle gets greater.

https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html

here's some pictures of what i did with this interactive angle generator.

the picturss show an angle of 0, 30, 45, 60, 85, and 90 in that order.

on the unit circle, the radius of the circle is always equal to 1 which means that the hypotenuse of the right triangle formed is always equal to 1.

the the length of the horizontal line formed is always equal to x.

the length of the vertical line formed is always equal to y.

consequently, the trig functions become:

sin(angle) = opposite / hypotenuse = y/1 = y

cos(angle) = adjacent / hypotenuse = x/1 = x

tan(angle) = opposite / adjacent = y/x

when the angle is equal to 90 degrees, y is equal to 1 and x is equal to 0.

consequently,

sin(90) = y/1 = 1/1 = 1

cos(90) = x/1 = 0/1 = 0

tan(90) = y/x = 1/0 = undefined.

that's your solution.

just replace 90 degrees with pi/2 radians and you get the result you are looking for.

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