Find the exact value of the trigonometric function. Do not use a calculator.

cot⁡(-5π/4)

Question

Find the exact value of the trigonometric function. Do not use a calculator.

cot⁡(-5π/4)

shamil98 · Answer

consult the unit circle, friend.

anonymous · Answer

how?

astrophysics · Answer

|dw:1447390718623:dw| note this is the triangle for pi/4

jchick · Answer

attachment

astrophysics · Answer

and cotangent is $$cotx = \frac{ adj }{ opp }$$

astrophysics · Answer

5*pi/4 is in the second quadrant so use the triangle

jchick · Answer

I started by converting radians to degrees.
-5pi/4 = (-5(180))/4

jchick · Answer

After that first step, I had -225 degrees.
I went clockwise -225 degrees around my pretend graph until I got to a 45 degree angle in the upper left quadrant. This line allowed me to make an imaginary 45-45-90 triangle. The side lengths of  this type of triangle are  a, a, and asqrt(2). My sign chart/pretend graph has a window of (-1,1). The one side of the triangle would  equal -1. The side adjacent to it would be positive 1, however,  because it is above the x axis. The hypotenuse would equal sqrt(2). Cot is the opposite of tangent. Using SOHCAHTOA I figured Cot=adjacent/opposite. This gave me my answer of -1.