PPT-4.4 Graphs of Sine and Cosine: Sinusoids

By the end of today you should be able to Graph the sine and cosine functions Find the amplitude period and frequency of a function Model Periodic behavior with sinusoids Unit Circle The Sine Function y .   Hyperbolic sine (pronounced \sinsh"): e x (Note that this is dierent from cos(x).) dx Important identity:cosh 2 (x) sinh 2 (x)=1 Proof:  x 2  x 2 2 (x) sinh 2 (x)= 4 e 2x +2 Sec. . 4.6b. Exploration 1: Investigating Sinusoids. Graph these functions, one at a time, in the viewing window. . Which ones appear to be sinusoids?. Only these functions appear to be sinusoids!!!. Convert 105 degrees to radians. Convert 5. π. /9 to radians. What is the range of the equation y = 2 + 4cos3x?. 7. π. /12. 100 degrees. [-2, 6]. Derivatives of Trigonometric Functions. Lesson 3.5. Objectives. Find sin (-5. ). Find the values of . ϴ. for which . cos. . ϴ. =1 is true.. Graph the function y = sin x for the interval .  . Lesson 6-4 Amplitude and Period of Sine and Cosine Functions. Objective: To find the amplitude and period of sine and cosine functions..   To find out how high . Juanisha. climbed . up stairs, . you need to know more about the relationship between the ratios of the sides of a right triangle and the slope angle. .. Use . two different strategies to determine . 06.10.2011. 2.2. . Sinusoids. A sinusoids is signal that has the form of the . sine. or . cosine. function.. Consider the sinusoidal voltage.. 2.2. . Sinusoids. as a . function. of . ω. t. as a . Math 5. Learning Objectives for Unit. Learning Objectives for Unit. Assessment. All objectives will be rated from 0 – 7. 0 – 1. No data to assess or demonstrates minimal knowledge of learning objective, no mathematical practices used . Introduction- . Finding lengths. Sin, cos or tan to find lengths?. Finding missing lengths worksheet. Finding the Area of Triangles and Segments. The Sine rule. The Cosine Rule. The Sine and Cosine Rule (quiz and worksheet). Copyright: The ideas presented here and their implementation are the intellectual property of Cosine UK, to which we shall exercise our rights as the authors. . Direct or indirect imitation or use of any of the ideas or other documentation or their implementation is not permitted until we have issued our prior written permission. Unit 39. Potential Sine-on-Random Environments. Helicopter Vibration. Propeller-driven Aircraft. Gunfire. Launch Vehicle with Thrust Oscillation. Mil-Std-810G addresses some of these scenarios. Sine-on-Random Analysis and Testing. And Visa Versa. . Suppose: v. 1. (t) = 1V sin (. w. t). . v. 2. (t) = 1V . cos. (. w. t). The sine wave reaches its maximum when . w. t = 90. o. , but the cosine reaches its maximum when . w. t = 0. Unit . 3. 2. Vibrationdata. Sine Sweep Testing Purposes. Sine Sweep Testing of Components and Systems. Identify natural frequencies and amplification factors or damping ratios. Perform sine sweep before and after random vibration test to determine if any parts loosened, etc.. Lesson 6.1 – Functions that model a vibrating spring, an electrical current, and the horizontal range of a kicked soccer ball involve the two most important trigonometric functions. In the unit c Sin 0°= . Sin . = . Sin . π. =. Sin . =. Sin 2. π. =.  . Chapter 4. Graphs of the Circular Functions. Section 4.1. . Graphs . of the Sine and . Cosine . Functions. Objective:. SWBAT graph the sine and cosine functions with variations in amplitude and periods. .