Now that you are familiar with the unit circle, let us show you that just like the right triangle, the unit circle can be used to find sin(45 degrees) and also cos(45 degrees)
In the lesson about tangent ratio and sine ratio, we also used a 45 degrees triangle.
What do you remember about the lengths of the legs ? For a right triangle that has a 45 degrees angle, the legs have the same length. This means that x = y
We can again use the Pythagorean theorem to find x and y.
x^{2} + y^{2} = 1^{2}We can see that whether we use the right triangle only or the unit circle, we get the same answer. Since trigonometry means the measurement of triangles, you may have wondered so far why we use the unit circle to do trigonometry. Again, we get the same answer. Moreover, using the right triangle only has its limitations.
With the right triangle only, all angles must be positive while with the unit circle, angles could be negative.
Some values are hard to find with the right triangle although not impossible. For example, using the triangle below, what is sin (90 degrees) or cos(90 degrees)?
You could do what this teacher
is doing on this video to find these values. However, since his method
involves an imaginary angle of 0 degrees and as a result, this figure is
no longer a triangle, you are better off unit the unit circle.
On the unit circle, the sine of any angle is equal to the y-value, so sin(90 degrees) = 1
Similarly, the cosine of any angle is equal to the x-value, so cos(90 degrees) = 0
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.
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
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.