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Trigonometric Functions and Their Properties

Trigonometric Functions and Their Properties

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Ethan Morris

FREE Resource

The video tutorial revisits previous concepts and addresses confusion around solving a quadratic equation involving tan functions. It explains two methods to handle domain issues: shifting the tan curve and multiplying first. The instructor recommends the shifting method for its simplicity and consistency. The video concludes with a discussion on the importance of understanding periodic functions and their implications in solving equations.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What was the initial step taken after introducing the t results?

Converting to a quadratic equation

Finding the derivative

Solving a linear equation

Graphing the function

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why was one of the solutions considered invalid in the modified domain?

It was too large

It was negative

It was complex

It was zero

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period of the regular tan function?

π

π/2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first method, what operation is performed after shifting the answer?

Adding a constant

Subtracting pi

Multiplying by two

Dividing by two

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the coefficient of 1/2 in tan(x/2) do to the period of the function?

Halves the period

Doubles the period

Keeps the period the same

Triples the period

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is adding 2π considered in the second method?

To adjust for a phase shift

To eliminate negative values

To account for the full period of the modified tan function

To simplify the equation

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which method does the instructor recommend for adjusting the solution?

Using a numerical solver

Using a graphical approach

Multiplying first, then adding

Adding first, then multiplying

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