Convert to Radians and Degrees
Learn how to convert angles to radians and degrees. Practice with examples like -80 and 450 degrees. Explore graphs of sine and cosine functions, understand the period and amplitude, and sketch sine curves. Discover the differences between the sine and cosine functions in trigonometry.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Warm Up Convert to radians/degrees. ?? ? ?? ? 1) -80 2) 450 3) ?? 4) ?? ??? ??? ? ?
13-4 The Sine Function ? = sin? Today s Objective: I can graph the sine function.
? ? = sin? x 0 ? 6 ? 2 5? 6 ? y
? = sin? OR ? = sin? Domain: All real numbers Range: 1 y 1 Period: 2 Amplitude: 1
Period of a Sine Curve ?1= sin? ?3= sin.5? ?2= sin4? Calculator [MODE]: Radians [WINDOW] Xmin = 0 Xmax = 2 Xscl = /2 Ymin = 2 Ymax = 2 Yscl = 0.5 b = # of cycles from 0 to 2 Period of function = 2? ? = sin?? ?
Amplitude of a Sine Curve ?1= sin? ?3= 2sin? ?2= 2sin? Calculator [MODE]: Radians [WINDOW] Xmin = 0 Xmax = 2 Xscl = /2 Ymin = 2 Ymax = 2 Yscl = 0.5 ? = amplitude (stretch) a = reflects graph across x-axis ? = ?sin?
Find amplitude and period for each equation. 1.? = 2sin3? Amplitude = Period = 2. ? =1 2sin? 1 2 or 0.5 Amplitude = 4 2? 3 2 2? 0.25 Period = = 8? 3.. Amplitude = 3 4? 3 =2? Period = ? Write an equation for the graph. ? = 3sin3 2?
Sketching a Sine Curve Graph Amplitude = 2 1. Find amplitude and period. 2. Plot 5 points: Midline points Beginning, End Middle Amplitude points Max Min 2? 2 ? = 2sin2? = ? Period = 3. Sketch curve. 5 points: midline max midline min midline
Sketching a Sine Curve Graph Amplitude = 1.5 ? = 1.5sin? 1. Find amplitude and period. 2. Plot 5 points 3. Sketch curve. 2? ? 2 2? Period = = 4 5 points: midline max midline min midline
13-5 The cosine Function ? = cos? Today s Objective: I can graph the cosine function.
? = cos? OR ? = ???? Domain: All real numbers Range: 1 y 1 Period: 2 How does this graph differ from y = sin x? Amplitude: 1 ? 2 Translated left by
Properties of Cosine Function ? = amplitude a = reflects graph across x-axis b = # of cycles from 0 to 2 Period of function = 2? ? = ?cos?? ? Sketch the graph of: 5 points: max midline min midline - max ? = ?cos? ? = ?.?cos?? ?
