Express each value as a trigonomic function of an angle in quadrant I: Cot(-660)

adding 720º to our angle would give us a coterminal angle.

-660 + 720 = 60
so cot(-660) = cot 60
= 1/tan60
= 1/(√3/1) = 1/√3

Use the given information to determine the exact trigonometric value of csc(theta) if cot(theta)=-8 and 3pi/2 < theta < 2pi

To express a trigonometric function of an angle in a specific quadrant, we need to find a reference angle within that quadrant and then determine the sign of the trigonometric function based on the quadrant.

In this case, we want to express the value of cot(-660) as a trigonometric function of an angle in quadrant I.

To find the reference angle, we can add or subtract multiples of 360 degrees to the given angle until we obtain an angle within the range of 0 to 360 degrees.

For cot(-660), let's add multiples of 360 degrees until we get an angle in quadrant I:
-660 + 360 = -300 (angle within quadrant IV)
-300 + 360 = 60 (angle within quadrant I)

So, the reference angle for cot(-660) within quadrant I is 60 degrees.

Now we can determine the trigonometric function based on the reference angle. In this case, the cotangent (cot) is the reciprocal of the tangent (tan) function.

In quadrant I, the value of tan(60 degrees) is √3.

Therefore, in quadrant I:
cot(-660) = cot(60 degrees) = 1 / tan(60 degrees) = 1 / √3.

So, cot(-660) in quadrant I can be expressed as 1 / √3.