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.
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 + y21 = 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
-
Overtime Calculator - How much for Time and a Half or Double rate ?
Jan 18, 19 10:53 AM
This overtime calculator will help you figure out how much money earned for working overtime
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Recent Articles
-
Overtime Calculator - How much for Time and a Half or Double rate ?
Jan 18, 19 10:53 AM
This overtime calculator will help you figure out how much money earned for working overtime
-
Convert Square Feet to Acres Calculator
Jan 14, 19 09:22 AM
Convert square feet to acres and acres to square feet with this conversion calculator
-
Convert Kilograms to Tons calculator
Jan 13, 19 03:47 PM
Convert kilograms to tons and tons to kilograms with this conversion calculator
-
How to Convert Square Feet to Acres
Dec 14, 18 04:05 PM
Here is how to convert square feet to acres - To convert square feet to ...
-
Modeling Multiplication
Nov 15, 18 05:01 PM
Modeling multiplication with number counters - Learning multiplication is fun!
-
Properties of Congruence
Nov 09, 18 09:40 AM
Learn the three properties of congruence. Examples to illustrate which property.
-
Compound Interest Word Problems and Solutions
Nov 07, 18 02:38 PM
Practice with these well chosen compound interest word problems
Recent Lessons
-
Overtime Calculator - How much for Time and a Half or Double rate ?
Jan 18, 19 10:53 AM
This overtime calculator will help you figure out how much money earned for working overtime
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Tough Algebra Word Problems.
If you can solve these problems with no help, you must be a genius!
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.
