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. Find water left in a tank using arithmetic sequences

    Jul 20, 17 10:41 PM

    A water tank is emptied at a constant rate. Initially, 36,000 gallons of water were in the tank. A the end of five hours, 16,000 gallons remained. How

    Read More

New math lessons

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

            Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape








Recent Lessons

  1. Find water left in a tank using arithmetic sequences

    Jul 20, 17 10:41 PM

    A water tank is emptied at a constant rate. Initially, 36,000 gallons of water were in the tank. A the end of five hours, 16,000 gallons remained. How

    Read More