Unit 4A

Trigonometry Part 1

Lesson 1: Trigonometry Review

Converting all of the angles on the unit circle from degrees to radians results in the following:

Click here to download a printable version of the unit circle. Note this version has both degree and radian units shown for your reference.

Note that special triangles, in combination with the CAST Rule, can also be used to determine the exact values of the trigonometric ratios for angles given in radians. Converting the angles to radians gives the following reference triangles.

Using radians, instead of degrees, makes it possible to relate angle measures and arc lengths (linear measures). In radians, a central angle measure of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»1«/mn»«/mstyle»«/math» unit corresponds to a subtended arc of length «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»1«/mn»«/mstyle»«/math» unit.


If a number line was wrapped counter-clockwise around a unit circle, starting at the point «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced»«mrow»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mn»0«/mn»«/mrow»«/mfenced»«/mstyle»«/math», the length of the arc subtended by the central angle is the radian measure of the angle.

Radian measurement will become an important concept when graphing trigonometric functions since one unit on the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math»-axis is the same as one unit on the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-axis. This is not the case when using degrees as the vertical axis is usually adjusted so that the entire graph can be seen.

Moving forward in Math 31, when working with trigonometric functions, all angle measures will be in radians.