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 $$\text{cos}(2x) = 2\text{cos}^2(x) - 1$$ .

Solving Trigonometric Equations Flashcards

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15 questions

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1.

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

2.

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

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

6.

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

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

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