Question

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

\[\cot(\frac{ -5\pi }{ 4 })\]

How do you do so without a calculator?
Does cotangent have it's own number or something?
Please explain..

Answer 1

The "opposite" of cotangent is tangent. So if we are looking at the cotangent of a value, we can flip it to find the tangent. So the tangent of the above angle is \[-\frac{ 4\pi }{ 5 }\]

Answer 2

Convert that to degrees so you can see what youre looking at in something other than radians. That radian measure is the same as -144 degrees.

Answer 3

\[\cot \left( \frac{ -5 \pi }{ 4 } \right)=-\cot \left( \frac{ 5 \pi }{ 4 } \right)=-\cot \left( \pi+\frac{ \pi }{ 4 } \right)=-\cot \frac{ \pi }{ 4 }=-1\]

Answer 4

How do you convert radians into degrees?

Answer 5

\[\pi ~ radians=180 ~degree\]

Answer 6

Ooooh I see.
Also, where exactly did the 5 go when you did -cot(pi + (pi/4))

Answer 7

take 4 L,C,M and then you will see they are equal.

Answer 8

\[\pi +\frac{ \pi }{ 4 }=\frac{ 4 \pi+ \pi }{ 4 }=\frac{ 5 \pi }{ 4 }\]

Answer 9

I see.
Thank you @surjithayer and @IMStuck ♥

Answer 10

yw