Download presentation

Presentation is loading. Please wait.

Published byKeanu Blakely Modified over 2 years ago

1
Graphs of the Sine, Cosine, & Tangent Functions Objectives: 1. Graph the sine, cosine, & tangent functions. 2. State all the values in the domain of a basic trigonometric function that correspond to a given value of the range. 3. Graph the transformations of sine, cosine, & tangent functions. 7.1

2
Graphing the Cosine Function on the Coordinate Plane DegreesRadianscos(t) 0°01 30°.866 45°.707 60°.5 90°0 120°-.5 135°-.707 150°-.866 180° 210°-.866 225°-.707 240°-.5 270°0 300°.5 315°.707 330°.866 360°1

3
Graphing the Sine Function on the Coordinate Plane

4
Characteristics of the Sine & Cosine Functions Period :2π Domain:The set of all real numbers (−∞, ∞) Range:[−1, 1] Function Type: Sine (Odd) Cosine (Even) The period of a function is the amount of time or length of a complete cycle. In other words, how long until the graph starts repeating. For the sine and cosine functions, the period is the same. Remember: Even Functions are symmetric about the y-axis, Odd Functions are symmetric about the origin (shown below).

5
Example #1 State all values of t for which sin(t) = 1. Remember that sine, the y- coordinate, is 1 at 90°. Any angle coterminal with that is also a solution. (1,0) (0,1) (0,-1) (-1,0)0°, 360° 90° 180° 270°

6
Example #2 State all the values of t for which cos(t) = Remember that cosine, the x-coordinate, is -½ at 120° and 240°. Any angle coterminal with those are also a solutions. (1,0) (0,1) (0,-1) (-1,0)0°, 360° 90° 180° 270°

7
Graphing the Tangent Function on the Coordinate Plane

8
Characteristics of the Tangent Function Period:π Domain:All real numbers except odd multiples of Range:All real numbers (−∞, ∞) Function Type: Odd

9
Example #3 State all values of t for which tan(t) = 1. Tangent is 1 where sine and cosine values are the same. This occurs at 45° and 225°. The cycle is shorter for tangent though, so to specify all solutions we only need to add 180° to our original solution.

10
Basic Transformations of Sine, Cosine, & Tangent Vertical Stretches Vertical stretches or compressions by a factor of “a”. Reflections Reflections over the x-axis. Vertical Shifts Vertical shifting of “b” units.

11
Example #4 List the transformation(s) and sketch the graph. Vertical stretch by a factor of 2.

12
Example #5 List the transformation(s) and sketch the graph. Vertical compression by a factor of 1/3 and x- axis reflection.

13
Example #6 List the transformation(s) and sketch the graph. Vertical shift of four units down.

Similar presentations

OK

Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Unit Circle Approach.

Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Unit Circle Approach.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on mass media services Ppt on indian army weapons images Ppt on observation method of data collection Ppt on indian textile industries in usa Ppt on election commission of india Ppt on microsoft excel 2007 Ppt on cross site scripting definition Ppt online compressor software Ppt on library management system download Ppt on quality education basketball