What is the general solution for the equation $$\tan(\theta) = k$$ ?

The general solution is $$\theta = \tan^{-1}(k) + n\frac{\theta}{2}$$ , where $$n$$ is any integer.

How do you solve the equation $$\frac{1}{2} = \frac{\text{sin}(\theta)}{1}$$ ?

To solve, find the angle(s) where $$\text{sin}(\theta) = \frac{1}{2}$$ , which are $$\theta = \frac{\text{\text{pi}}}{6} + 2n\text{\text{pi}}$$ and $$\theta = \frac{5\text{\text{pi}}}{6} + 2n\text{\text{pi}}$$ .

What are the values of $$\text{sin}(\theta)$$ and $$\text{cos}(\theta)$$ at $$\theta = 0$$ ?

$$\text{sin}(0) = 0$$ and $$\text{cos}(0) = 1$$ .

How do you find the solutions for $$\text{cos}(\theta) = 0$$ in the interval $$[0, 2\text{pi})$$ ?

The solutions are $$\theta = \frac{\text{pi}}{2}$$ and $$\theta = \frac{3\text{pi}}{2}$$ .

What is the period of the sine function?

The period of the sine function is $$2\text{pi}$$ .

What is the difference between the sine and cosine functions?

Sine and cosine are both periodic functions, but sine represents the y-coordinate of a point on the unit circle, while cosine represents the x-coordinate.

How do you solve $$\text{sin}(\theta) = -\frac{1}{2}$$ for $$0 \text{ to } 2\text{pi}$$ ?

The solutions are $$\theta = \frac{7\text{pi}}{6}$$ and $$\theta = \frac{11\text{pi}}{6}$$ .

What is the cotangent function?

The cotangent function is the reciprocal of the tangent function, defined as $$\text{cot}(\theta) = \frac{\text{cos}(\theta)}{\text{sin}(\theta)}$$ .

What is the relationship between the angles in a right triangle and trigonometric functions?

In a right triangle, the sine, cosine, and tangent functions relate the angles to the ratios of the lengths of the sides.

How do you solve $$\text{tan}(\theta) = 1$$ for $$0 \text{ to } 2\text{pi}$$ ?

The solutions are $$\theta = \frac{\text{pi}}{4}$$ and $$\theta = \frac{5\text{pi}}{4}$$ .

What is the significance of the angle $$\frac{\text{pi}}{2}$$ in trigonometry?

The angle $$\frac{\text{pi}}{2}$$ (90 degrees) corresponds to the maximum value of the sine function and the minimum value of the cosine function.

Resource Library

Math

Trigonometry

Trigonometric Equations

Lesson 17 Solving Trigonometric Equations

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF.TF.B.7, HSF.TF.A.2, HSF.TF.A.4

Standards-aligned

Wayground Content

FREE Resource

Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is a trigonometric equation?

Back

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically an angle, such as sine, cosine, or tangent.

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1, inclusive.

Tags

CCSS.HSF.TF.A.4

FLASHCARD QUESTION

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane, used to define trigonometric functions.

Tags

CCSS.HSF.TF.A.2

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.2

FLASHCARD QUESTION

Front

What is the Pythagorean identity?

Back

Tags

CCSS.HSF.TF.C.8

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

Roundtable 2025

Flashcard

•

KG - University

15 questions

PART 2-PA First Semester Review-December 2024

Flashcard

•

8th Grade - University

15 questions

Unit II Test Review Bio A (Ch. 3-5)

Flashcard

•

9th - 11th Grade

15 questions

Wishes and regrets

Flashcard

•

8th - 12th Grade

7 questions

Respiration

Flashcard

•

8th Grade - University

15 questions

7th PBA Test #4 Review

Flashcard

•

7th Grade - University

10 questions

Printing Press

Flashcard

•

9th - 12th Grade

12 questions

Trennbare Verben

Flashcard

•

Popular Resources on Wayground

10 questions

5.P.1.3 Distance/Time Graphs

Quiz

•

5th Grade

10 questions

Fire Drill

Quiz

•

2nd - 5th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

22 questions

School Wide Vocab Group 1 Master

Quiz

•

6th - 8th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

20 questions

Inferences

Quiz

•

4th Grade

12 questions

What makes Nebraska's government unique?

Quiz

•

4th - 5th Grade

Discover more resources for Mathematics

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

20 questions

Exponential Functions Key Features

Quiz

•

9th Grade

11 questions

Adding and Subtracting Polynomials

Quiz

•

9th Grade

12 questions

Exponential Growth and Decay

Quiz

•

9th Grade

20 questions

Box and Whisker Plots

Quiz

•

9th Grade

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

15 questions

Graphing Inequalities

Quiz

•

7th - 9th Grade

21 questions

Factoring Trinomials (a=1)

Quiz

•

9th Grade