SOLUTION: If cot(x)=-2 and cos(x)>0 find the exact value of cos(x/2) I tried working it out based on where it would be on the graph from the cot(x) value and the Cos(x) being greater the

Algebra ->  Trigonometry-basics -> SOLUTION: If cot(x)=-2 and cos(x)>0 find the exact value of cos(x/2) I tried working it out based on where it would be on the graph from the cot(x) value and the Cos(x) being greater the      Log On


   



Question 1056115: If cot(x)=-2 and cos(x)>0 find the exact value of cos(x/2)
I tried working it out based on where it would be on the graph from the cot(x) value and the Cos(x) being greater then 0
From there I tried to use conversions and just got lost. Any help to figure this out would be great.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
First value tells you that cosine%28x%29%2Fsin%28x%29%3C0 and that means quadrant 2 or quadrant 4. Second part, cosine%28x%29%3E0 means quadrant 1 or quadrant 4. The conclusion to make for what is common, is x is in quadrant 4.

You can draw a simple right triangle with radius endpoint in the quadrant 4 to help you further. Radius, or hypotenuse, is 1; horiZontal coordiante 2*k; vertical component or coordinate -1*k. You can also say, tan%28x%29=-1%2F2.

x is arc whose tangent is negative one-half.