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Trigonometric Functions and Their Properties

Trigonometric Functions and Their Properties

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

This lesson covers solving double angle equations in trigonometry, focusing on sine, cosine, and tangent functions. It begins with an introduction to the concept, followed by a graphical investigation using sine and cosine graphs to understand transformations and periods. The lesson includes three examples demonstrating algebraic solutions for double angle equations, highlighting the importance of understanding periodic functions and transformations.

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8 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main focus of lesson six in the advanced functions course?

Understanding quadratic functions

Solving double angle equations

Solving linear equations

Graphing polynomial functions

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the transformation parameter K affect the graph of y = sin(x)?

It affects the vertical shift

It changes the amplitude

It performs horizontal stretches and compressions

It alters the phase shift

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period of the function y = sin(2x)?

π/2

π

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many solutions are there for sin(x) = 1/√2 between 0 and 2π?

Three

Two

Four

One

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the number of solutions when the period of a function is halved?

The number of solutions is halved

The number of solutions is tripled

The number of solutions remains the same

The number of solutions is doubled

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Example 1, what is the first step in solving sin(2θ) = √3/2?

Directly solve for θ using inverse sine

Change the equation to a linear trig equation using a let statement

Graph the function to find intersections

Use a calculator to find approximate solutions

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period of a tan double angle function?

π/2

π

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