Unit 2

Trigonometry

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Part 2.4B corresponds to section 6.2, starting on page 299 of your Pre-Calculus 12 textbook.

The Sine of a Sum of Angles Identity

The derivations of reciprocal, quotient, and Pythagorean identities used the unit circle, and were relatively straightforward. Determining a formula for the sine of a sum of angles is more involved and can be done using the right triangle definitions of sine and cosine. You do not need to be able to reproduce this derivation, but you should be able to follow the reasoning.

Draw a right triangle inside a rectangle and label it as shown. Let the hypotenuse of the triangle be «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»1«/mn»«/mstyle»«/math».


Let «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mo»§#8736;«/mo»«mi»B«/mi»«mi»A«/mi»«mi»C«/mi»«mo»=«/mo»«mo»§#945;«/mo»«/mrow»«/mstyle»«/math»and «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mo»§#8736;«/mo»«mi»C«/mi»«mi»A«/mi»«mi»E«/mi»«mo»=«/mo»«mo»§#946;«/mo»«/mrow»«/mstyle»«/math».