section 6.2 trigonometric functions: unit circle...
TRANSCRIPT
Section 6.2
Trigonometric Functions:
Unit Circle Approach
Copyright © 2012
Copyright © 2012
Copyright © 2012
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2 2,2 2
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Make a second congruent triangle.
Use Pythagorean Theorem to find b.
This triangle is equilateral so all sides are 1. 2a = 1 so a = . 1
2
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the exact value of each expression.3 5 9(a) cos135 (b) tan (c) sin 225 (d) cos (e) sin4 4 4π π π ° ° −
2 2 2(a) The point , corresponds to 35 so cos 1352 2 2
− ° ° = −
2 2 3(b) The point , corresponds to 2 2 4
23 2so tan 14 2
2
π
π
−
= = −−
Find the exact value of each expression.3 5 9(a) cos135 (b) tan (c) sin 225 (d) cos (e) sin4 4 4π π π ° ° −
2 2 2(c) The point , corresponds to 225 so sin 2252 2 2
− − ° ° = −
2 2 5 5 2(d) The point , corresponds to so cos2 2 4 4 2
π π − − − = −
2 2 9(e) The point , corresponds to 2 2 4
9 2so sin4 2
π
π
=
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
4 7Find: (a) cos 150 (b) sin ( 30 ) (c) tan (d) sin3 6π π ° − °
5 3(a) cos 150 cos6 2π
° = = −
1(b) sin ( 30 ) sin6 2π − ° = − = −
34 2(c) tan 313
2
π −= =
−
7 1(d) sin6 2π = −
Your calculator has buttons for sin, cos, and tan so to find values of the remaining 3 trigonometric functions we use:
CHANGE MODE TO RADIANS
2 24 and 3 so 16 9 5a b r a b= = − = + = + =