How do you solve the equation $$-2\text{sqrt}{3} = -4\text{cos} x$$ ?

Divide both sides by -4 to get $$\text{cos} x = \frac{\text{sqrt}{3}}{2}$$ . The solutions are $$x = \frac{\text{pi}}{6}, \frac{11\text{pi}}{6}$$ .

How do you simplify $$\frac{\tan\theta+\text{cot}\theta}{\tan\theta}$$ ?

This simplifies to $$\text{csc}^2\theta$$ .

What is the Pythagorean identity involving sine and cosine?

$$\text{sin}^2 \theta + \text{cos}^2 \theta = 1$$ .

How do you solve the equation $$1 + 2\text{sin} x = \text{csc} x$$ ?

Rearranging gives $$\text{sin}^2 x + 2\text{sin} x - 1 = 0$$ . The solutions are $$x = \frac{\text{pi}}{6}, \frac{5\text{pi}}{6}, \frac{3\text{pi}}{2}$$ .

What is the definition of cosecant?

$$\text{csc} \theta = \frac{1}{\text{sin} \theta}$$ .

How do you solve $$3\text{csc}^2x = 4 + 2\text{csc}^2x$$ ?

Rearranging gives $$\text{csc}^2x = 4$$ . The solutions are $$x = \frac{\text{pi}}{6}, \frac{5\text{pi}}{6}, \frac{7\text{pi}}{6}, \frac{11\text{pi}}{6}$$ .

What is the range of the sine function?

The range of the sine function is [-1, 1].

What is the definition of secant?

$$\text{sec} \theta = \frac{1}{\text{cos} \theta}$$ .

What is the relationship between sine and cosecant?

$$\text{sin} \theta = \frac{1}{\text{csc} \theta}$$ .

What is the solution set for $$\text{sin} x = 0$$ ?

The solutions are $$x = n\text{pi}$$ , where n is any integer.

Precalc: Solving Trig Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the general form of a trigonometric equation?

Back

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically expressed in the form f(x) = g(x), where f and g are trigonometric functions.

Tags

CCSS.HSF.TF.B.7

2.

FLASHCARD QUESTION

Front

What is the range of the cosine function?

Back

The range of the cosine function is [-1, 1].

Tags

CCSS.HSF-IF.C.7E

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

4.

FLASHCARD QUESTION

Front

What is the identity for cosecant in terms of sine?

Back

Tags

CCSS.HSF.TF.C.8

5.

FLASHCARD QUESTION

Front

What is the relationship between tangent and cotangent?

Back

Tags

CCSS.HSF.TF.A.2

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

There is no solution.

Tags

CCSS.HSF.TF.B.7

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