SOLUTION: Use the trigonometric function values of the quadrant angles to evaluate. 7 cot 270 degrees + 3 cos 180 degrees.

Algebra ->  Trigonometry-basics -> SOLUTION: Use the trigonometric function values of the quadrant angles to evaluate. 7 cot 270 degrees + 3 cos 180 degrees.      Log On


   

Question 898836: Use the trigonometric function values of the quadrant angles to evaluate.
7 cot 270 degrees + 3 cos 180 degrees.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
7*cot(270) = 0

3*cos(180) = -3

7*cot(270) - 3*cos(180) is equal to 0 + 3 which is equal to 3.

that's your solution.

i used a calculator.
if i didn't have a calculator, i would do the following.


reference angle for 270 degrees is equal to 90 because 180 + 90 = 270.
cot(90) = cos(90)/sin(90) = 0/1 = 0.
cot(90) = 0
270 is in between the third and fourth quadrant.
since the cotangent is equal to 0, the sign doesn't matter, so cot(270) = 0.

reference angle for 180 is equal to 0 because 180 - 180 = 0.
cos(0) = 1
180 degrees is between second and third quadrant.
cosine is negative when the angle is in between the second and third quadrant, so cos(180) = -1

therefore:

7*cot(270) - 3*cos(180) = 7*0 - 3*(-1) which is equal to 0 + 3 which is equal to 3.

the graphs of cot(270) and cos(180) are shown below:

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