What is the solution set for the equation $$(\text{cos}\, x - 1)(2\text{sin}\, x + 1) = 0$$ in the interval $$(0, 2\text{pi}]$$ ?

The solution set is $$\text{2\text{pi}, } \frac{7\text{pi}}{6}, \frac{11\text{pi}}{6}$$ .

How do you solve $$50\text{sin}^2x = 50 + 75\text{sin}x$$ ?

Rearrange to form a quadratic equation in terms of $$\text{sin}x$$ : $$50\text{sin}^2x - 75\text{sin}x - 50 = 0$$ . Use the quadratic formula to find $$\text{sin}x$$ , then solve for $$x$$ .

What are the solutions for $$50\text{sin}^2x = 50 + 75\text{sin}x$$ in the interval $$(0, 2\text{pi}]$$ ?

The solutions are $$\frac{7\text{pi}}{6}, \frac{11\text{pi}}{6}$$ .

What is the equation $$2\text{sin}\, x \tan x + 2\text{sin}\, x = 0$$ used for?

This equation can be factored to find solutions for $$\text{sin}\, x = 0$$ or $$\tan x = -1$$ .

What are the solutions for $$2\text{sin}\, x \tan x + 2\text{sin}\, x = 0$$ in the interval $$(0, 2\text{pi}]$$ ?

The solutions are $$\frac{3\text{pi}}{4}, \text{pi}, \frac{7\text{pi}}{4}, 2\text{pi}$$ .

What is the periodicity of the sine function?

The sine function has a periodicity of $$2\text{pi}$$ , meaning it repeats its values every $$2\text{pi}$$ radians.

What is the periodicity of the cosine function?

The cosine function also has a periodicity of $$2\text{pi}$$ , repeating its values every $$2\text{pi}$$ radians.

What is the tangent function's periodicity?

The tangent function has a periodicity of $$\text{pi}$$ , repeating its values every $$\text{pi}$$ radians.

What is a quadratic trigonometric equation?

A quadratic trigonometric equation is an equation that can be expressed in the form $$a\text{sin}^2x + b\text{sin}x + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the role of trigonometric identities in solving equations?

Trigonometric identities can simplify equations, allowing for easier manipulation and solution of the equation.

What is the sine double angle identity?

The sine double angle identity states that $$\text{sin}(2x) = 2\text{sin}(x)\text{cos}(x)$$ .

What is the cosine double angle identity?

The cosine double angle identity states that $$\text{cos}(2x) = \text{cos}^2(x) - \text{sin}^2(x)$$ or equivalently $$\text{cos}(2x) = 2\text{cos}^2(x) - 1$$ .

Resource Library

Math

Trigonometry

Trigonometric Equations

Solving Trigonometric Equations

Flashcard

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF.TF.B.7, HSF.TF.A.4, HSF.TF.C.9

Standards-aligned

Wayground Content

Used 1+ times

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. These equations can be solved for the variable to find the angle(s) that satisfy the equation.

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

What is the general approach to solving trigonometric equations?

Back

1. Isolate the trigonometric function. 2. Use trigonometric identities if necessary. 3. Solve for the angle(s). 4. Consider the periodic nature of trigonometric functions to find all solutions within the specified interval.

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

Back

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

What is the significance of the interval when solving trigonometric equations?

Back

The interval specifies the range of values for the variable (usually an angle) within which solutions must be found. It helps to limit the number of solutions to those that are relevant.

Tags

CCSS.HSF.TF.B.7

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

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

14 questions

Deviance

Flashcard

•

11th Grade

13 questions

Wives of Prophet Muhammad Flashcard

Flashcard

•

10th Grade - University

10 questions

Algebra

Flashcard

•

12th Grade

12 questions

E4 Final Exam: Biographies and Autobiographies (Smith)

Flashcard

•

12th Grade

12 questions

Biologi Tingkatan 5 Bab 3

Flashcard

•

12th Grade

9 questions

Tuesdays with Morrie

Flashcard

•

12th Grade

6 questions

PROBABILITY DISTRIBUTION

Flashcard

•

11th Grade

15 questions

LT 1.2-1.3 - Photosynthesis

Flashcard

•

11th - 12th Grade

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

10 questions

Factor Quadratic Expressions with Various Coefficients

Quiz

•

9th - 12th Grade

19 questions

Explore Probability Concepts

Quiz

•

7th - 12th Grade

43 questions

STAAR WEEK 1

Quiz

•

9th - 12th Grade

11 questions

Solving Quadratic Equations by Factoring

Quiz

•

9th - 12th Grade

20 questions

Solving quadratics using square roots

Quiz

•

11th Grade

10 questions

Trigonometric Ratios

Quiz

•

9th - 11th Grade

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

6 questions

Equations of Circles

Quiz

•

9th - 12th Grade