exact value of cot(-60)

Question

can someone please help me find the exact value of cot(-60)

Answer 1

Recall that tanθ = sinθ / cosθ.

 

cotθ is the reciprocal of that. 

 

Also, -60 degrees is in the 4th quadrant.  cosine is positive here and sine is negative here.

 

 

cot(-60)=

 

cos(-60) / sin(-60) = 

 

(1/2) / (-√(3) / 2) =

 

(1/2) * (-2 / √(3)) =

 

-1/√(3)

 

 

Rationalize the denominator.  Multiply the result by √(3) / √(3). We end up with

 

-√(3) / 3

 

Answer 2

 

cos (-60) = 0.5

 

 

based on the quadrant rule "All Student Takes Calculus", it represents the positive sign of sine, cosine, and tangent  in the four quadrants.

 

moving counterclockwise (start from the positive x-axis)

first quadrant - sin, cos, and tan are all positive

2nd quadrant - sin is positive only

3rd quadrant - tan is positive only

4th quadrant - cos is positive only

 

when the degree is positive, the angle is moving counterclockwise moving toward 1st quadrant start from positive x-axis.

 

when the degree is negative, the angle is moving clockwise moving toward the 4th quadrant start from positive x-axis.

 

since cos (degree) = cos (-60) means it will move clockwise and -60 will be in the 4th quadrant, the answer should be a positive due to the rule above.

 

so cos (-60) = cos(60) = 0.5