SOLUTION: what is cosθ= 1/root2 on the interval 0≤θ≤2π

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Question 920395: what is cosθ= 1/root2 on the interval 0≤θ≤2π
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
cosine(theta) = 1/sqrt(2)

you can use your calculator to see that theta = 45 degree, or you can recognize that 1/sqrt(2) is the same as sqrt(2)/2 after it is simplified and that sqrt(2)/2 is the sine and the cosine of 45 degree angle.

the cosine of the angle is positive in the first and fourth quadrant.

you already have the angle in the first quadrant.

that angle is 45 degrees.

the equivalent angle in the fourth quadrant is equal to 360 - 45 = 315 degrees.

so your angles are 45 degrees and 315 degrees in the interval between 0 degrees and 360 degrees.

translate all these to radians by using the conversion formula of radians = degrees * pi / 180 and you will get:

your angles are 1/4 * pi and 7/4 * pi in the interval between 0 radians and 2 * pi radians.