Chapter 14: Q3. (page 774)

Write the equation of a trigonometric function with a phase shift of $- 45 °$ .

Short Answer

Expert verified

The equation of the trigonometric function with a phase shift of $- 45 °$ is $y = \sin (θ + 45 °) + 2$ .

Step by step solution

Step 1. Write down the given information.

The given statement is to define the concept of midline of trigonometric graph.

Step 2. Concept used.

A function of the form:

$y = a \sin b (θ - h) + k, y = a \cos b (θ - h) + k and y = a \tan b (θ - h) + k$ has phase shift $(h)$ . And if $h > 0$ the phase shift is to the right and if $h < 0$ then the phase shift is to the left.

Step 3. Write the equation of the trigonometric function with a given phase shift.

With the help of concept stated above, the equation of trigonometric function with a phase shift of $- 45 °$ is written as:

$\begin{matrix} y = a \sin b (θ - h) + k \\ y = (1) \sin [1 (θ - (- 45 °))] + (2) .... (\begin{array}{l} Pluggingfor h = - 45 °, \\ a = 1, b = 1 and k = 2 \end{array}) \\ y = \sin (θ + 45 °) + 2 \end{matrix}$

Step 4. Conclusion.

The equation of the trigonometric function with a phase shift of $- 45 °$ is $y = \sin (θ + 45 °) + 2$ .

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Write the equation of a trigonometric function with a phase shift of $- 45 °$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Write the equation of the trigonometric function with a given phase shift.

Step 4. Conclusion.

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Write the equation of a trigonometric function with a phase shift of -45°.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Write the equation of the trigonometric function with a given phase shift.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Write the equation of a trigonometric function with a phase shift of $- 45 °$ .