if I have the sine, cosine, or tangent how do I find the reference angle in degrees?

Question

cos 0 = 1/2 how do I figure out the reference angle in degrees

Answer 1

If you know the sine and cosine values of a given angle, then you know the tangent.

So it's just a matter of determining the quadrant that is applicable.

 

Quadrant  Sines  Cosines

I                 +          +

II                +          -

III               -           -

IV               -           +

 

 

You figure out the reference angle by drawing a given angle with its initial side in the standard position (pointing eastward) and its terminal side landing wherever it must, after angular rotation counter clockwise by the stated amount.

 

The reference angle, always positive, is the acute angle between the terminal side and the horizontal axis.

 

For example the reference angle for 210 degrees is 30^o such that the hypotenuse of the reference triangle is one (the Unit Circle) and the 'legs' of the reference triangle are:

Vertical: -½, meaning sin 210⁰ 

Horizontal: -½√3, meaning cos 210^o

Answer 2

In addition to Kenneth's answer, I would like to show you a chart that explains why each trigonometric function is positive and negative in certain quadrants.

 

https://www.wyzant.com/resources/files/330953/trigonometric_functions_in_a_coordinate_system

Answer 3

cos θ = 1/2

θ = π/3

 

This is one of the values of the 30-60-90 triangle.

Memorizing all of them shall be very helpful.