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
Sep 18, 19 01:16 PM
Factoring using the box method. Common pitfalls to avoid when using this method.
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Recommended
Scientific Notation Quiz
Graphing Slope Quiz
Adding and Subtracting Matrices Quiz
Factoring Trinomials Quiz
Solving Absolute Value Equations Quiz
Order of Operations Quiz
Types of angles quiz
Sep 18, 19 01:16 PM
Factoring using the box method. Common pitfalls to avoid when using this method.