Question

What is the reference angle and cosine of StartFraction 7 pi Over 6 EndFraction ?

StartFraction pi Over 6 EndFraction, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction pi Over 6 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction pi Over 3 EndFraction, negative one-half
StartFraction pi Over 3 EndFraction, one-half

Answer 1

Answer:

Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.

Step-by-step explanation:

Answer 2

We will see that the reference angle is pi/6, and the cosine of that angle is:

cos(pi/6) = 0.866

How to find the reference angle?

Here we know that, measuring from the positive x-axis, the angle measures (7/6)*pi.

The reference angle is measured, in this case, from the closest axis, which is the negative x-axis.

To get the measure, we need to take the angle measured from the positive x-axis and subtract the angle between the positive and negative x-axis, which is pi.

Then we have:

θ = (7/6)*pi - pi = (1/6)*pi

Now we just need to take the cosine of that angle, we will get:

cos(pi/6) = 0.866

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