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What are the graphs and important properties of the graphs of \(y = \cos(x)\) and \(y = \sin(x)\)? What are the domains of the sine and cosine functions? What are the ranges of the sine and cosine functions?
- 5.5: Graphs of the Sine and Cosine Functions
Learning Objectives. Graph variations of sinusoidal...
- 5.5: Graphs of the Sine and Cosine Functions
12 kwi 2024 · Learning Objectives. Graph variations of sinusoidal functions \ (y=\sin ( x )\) and \ (y=\cos ( x )\). Identify properties of a sinusoidal graph: amplitude, period, vertical shift, and phase shift. Construct a sinusoidal equation from a graph or a description.
4 mar 2023 · Which of the following equations are identities? a \(\sin 2 \alpha=2 \sin \alpha\) b \(\cos (x+1)=\cos x\) Answer. a Compare the graphs of \(Y_1=\sin 2 x\) and \(Y_2=2 \sin x\). Enter the two equations in the ZTrig window and press ZOOM 7 to see the graphs shown below.
The Trigonometric Identities are equations that are true for Right Angled Triangles. (If it isn't a Right Angled Triangle use the Triangle Identities page) Each side of a right triangle has a name: Adjacent is always next to the angle. And Opposite is opposite the angle.
To verify the trigonometric identities, we usually start with the more complicated side of the equation and essentially rewrite the expression until it has been transformed into the same expression as the other side of the equation.
Verify the fundamental trigonometric identities. Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.
How do you use the fundamental identities to prove other identities? Divide the fundamental identity # sin^2x + cos^2x = 1# by #sin^2x# or #cos^2x# to derive the other two: #sin^2x/sin^2x + cos^2x/sin^2x = 1/sin^2x#. #1 + cot^2x = csc^2x#. #sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x#. #tan^2x + 1 = sec^2x#.
