Determining trigonometric functions given their graphs - Graphing Trigonometric Functions

Determining trigonometric functions given their graphs

Basic Concepts
Sine graph: y = sin x
Cosine graph: y = cos x
Graphing transformations of trigonometric functions

Related Concepts
Ferris wheel trig problems
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems

Lessons

1.
For the following graph, write an equation (with the smallest phase shift) in the form of:
(i) y = a sin b(x - c) + d
(ii) y = - a sin b(x - c) + d
(iii) y = a cos b(x - c) + d
(iv) y = - a cos b(x - c) + d

Determining trigonometric functions given their graphs

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TrigonometrySine graph: y = sin x

TrigonometryCosine graph: y = cos x

TrigonometryGraphing transformations of trigonometric functions

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Sine graph: y = sin x

Cosine graph: y = cos x

Graphing transformations of trigonometric functions

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Lessons

1.

For the following graph, write an equation (with the smallest phase shift) in the form of: (i) y = a sin b(x - c) + d (ii) y = - a sin b(x - c) + d (iii) y = a cos b(x - c) + d (iv) y = - a cos b(x - c) + d

a)

b)

2.

A sinusoidal curve has a minimum point at (−π3,−5)\left( { - \frac{\pi }{3},\; - 5} \right)(−3π​,−5) and the closest maximum point to the right is (π6,3)\left( {\;\frac{\pi }{6},\;3} \right)(6π​,3). Determine an equation of this curve.

Determining trigonometric functions given their graphs

Don't just watch, practice makes perfect.

We have over 250 practice questions in Trigonometry for you to master.

Trigonometry
Sine graph: y = sin x

Trigonometry
Cosine graph: y = cos x

Trigonometry
Graphing transformations of trigonometric functions

or

For the following graph, write an equation (with the smallest phase shift) in the form of:
(i) y = a sin b(x - c) + d
(ii) y = - a sin b(x - c) + d
(iii) y = a cos b(x - c) + d
(iv) y = - a cos b(x - c) + d

A sinusoidal curve has a minimum point at $\left( { - \frac{\pi }{3},\; - 5} \right)$ and the closest maximum point to the right is $\left( {\;\frac{\pi }{6},\;3} \right)$ . Determine an equation of this curve.