THE UNIT CIRCLE

Hey everyone hope you had a fun Halloween and enjoyed your weekend! But remember to keep up with your homework and don't forget about Pre-Calculus.

THE UNIT CIRCLE

The "Unit Circle" is a circle with a radius of 1.

Using the unit circle makes it easy to find the values of trigonometric functions at quadrantal angles.                                                                                                                    

 For example, a 90º rotation from the positive x-axis puts you on the positive y-axis, which intersects the unit circle at the point (0, 1). From this, you know that (cos 90º, sin 90º) = (0, 1).

This is a graph of the values of all three trigonometric functions at each quadrantal angle:

Important Angles 30º , 45º , 60º

Most angles on the unit circle are based on the reference angles of either 30º , 45º , 60º

You should remember the special triangles from grade 11 , If not here is a labeled diagrams to help you.

Finding the missing side of a right triangles

Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2+b2=c2, which is known as the Pythagorean Theorem. The theorem states that the hypotenuse of a right triangle can be easily calculated from the lengths of the sides. The hypotenuse is the longest side of a right triangle.

If you're given the lengths of the two sides it is easy to find the hypotenuse. Just square the sides, add them, and then take the square root. Here's an example:

Since we are given that the two legs of the triangle are 3 and 4, plug those into the Pythagorean equation and solve for the hypotenuse:

a2+b2=c2

32+42=c2

9+16=c2

c=5

If you are given the hypotenuse and one of the legs it's going to be slightly more complicated, but only because you have to do some algebra first. Suppose you know that one leg is 5 and the hypotenuse (longest side) is 13. Plug those into the appropriate places in the Pythagorean equation:

a2+b2=c2

52+b2=132

25+b2=169

b2=144

b=12

Thank you for reading my blog post, I hope this post helped you review/ learn about the unit circle and the special triangles involved. 

-Ravinder Sehira 

sources: 

Pre-calculus 12 McGraw-Hill Ryerson- Text Book

Pre-Calculus 40s Unit 4 Circular Functions- Notes

sites:

http://www.freemathhelp.com/q6-right-triangle.html

http://www.mathsisfun.com/geometry/unit-circle.html

http://www.wyzant.com/resources/lessons/math/trigonometry/unit-circle