Using the unit circle to find cosine and sine of 30 degrees and 60 degrees

Since we are using the unit circle, we need to put the 30-60-90 triangle inside the unit circle.

Unit circle and the 30-60-90 degrees triangle


The radius of the circle is also the hypotenuse of the right triangle and it is equal to 1.

We have already seen in the previous lesson that the leg opposite the 30 degrees angle is half the hypotenuse. 

Again, we will find the length of vertical black line of the triangle using the pythagorean theorem.

Since 1/2 = 0.5, we will replace 1/2 with 0.5 in the formula to simplify the computation.

12 = 0.52 + y2

1 = 0.25 + y2

1 - 0.25 = 0.25 - 0.25 + y2

0.75 = y2

Since 0.75 = 3/4,   y = √ (3/4)

y = √(3) / √(4)

y = √(3) / 2

x = 1/2, y = √3 / 2 and t could be 30 or 60 degrees.

cos(30 degrees) = y / 1 = y = √3 / 2

cos(60 degrees) = x / 1 = x = 1 / 2

sin(60 degrees) = y / 1 = y = √3 / 2

sin(30 degrees) = x / 1 = x = 1 / 2





Recent Articles

  1. Equation of a Circle

    Feb 22, 17 01:53 PM

    What is the equation of a circle? How to derive the equation of a circle?

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.


Page copy protected against web site content infringement by Copyscape






Recent Articles

  1. Equation of a Circle

    Feb 22, 17 01:53 PM

    What is the equation of a circle? How to derive the equation of a circle?

    Read More