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This page is meant to serve as a quick overview of the graphs of the circular functions.
Cosine and Sine Functions
y = cos x | y = sin x |
Domain: (-∞,∞) | Domain: (-∞,∞) |
Range: [-1,1] | Range: [-1,1] |
Amplitude: 1 | Amplitude: 1 |
Period: 2π | Period: 2π |
Basic format of sine and cosine graph equations and what can be derived from them.
y = c + a sin b(x-d) or y = c + a cos b(x-d) | |
Amplitude: |a| | Period: 2π / b |
Verticle Translation: c units. | Phase Shift: d units. |
Instructions to graphing the function.
Step 1 | Find the information that can be derived from the equation, using the information provided above. |
Step 2 | Using your knowledge of a basic sine or cosine wave as viewable above, stretch or compress the graph as necessary to match the period and amplitude. |
Step 3 | Shift the graph according the the verticle translation and the phase shift as found in Step 1. |
And now you have the graph of the sine or cosine function. |
Secant and Cosecant Functions
y = sec x | y = csc x |
Domain: {x|x ≠ π/2 + nπ} where n is any integer. | Domain: {x|x ≠ π/2 + nπ} where n is any integer. |
Range: (-∞,-1] U [1,∞) | Range: (-∞,-1] U [1,∞) |
Amplitude: DNE | Amplitude: DNE |
Period: 2π | Period: 2π |
Instructions to graphing the function. These instructions apply to secant and cosecant equations that are in the form y = a csc bx or y = a sec bx
Step 1 | Graph the reciprocal function to use as a guide. Note: It is recommended that this is lightly sketched or drawn using dashed lines. |
Step 2 | Draw in the verticle asymptotes. Note: It is recommended that this is lightly sketched or drawn using dashed lines. |
Step 3 | Sketch in the graph of the function, using the graph drawn in step 1 and the boundries drawn in step 2 as guides. It should resmemble the images shown above for the secant and cosecant graphs. |
And now you have a sketch of the secant or cosecant function. |
Tangent and Cotangent Functions
y = tan x | y = cot x |
Domain: {x|x ≠ π/2 + nπ} where n is any integer. | Domain: {x|x ≠ π/2 + nπ} where n is any integer. |
Range: (-∞,∞) | Range: (-∞,∞) |
Amplitude: DNE | Amplitude: DNE |
Period: π | Period: π |