What is the first step in solving the equation $$\tan x \tan^2x = 2\tan x$$ ?

Subtract $$2\tan x$$ from both sides and then factor out $$\tan x$$ .

How do you solve the equation $$\frac{\tan x}{\tan^2x} = 2$$ ?

Multiply both sides by $$\tan^2x$$ to eliminate the fraction.

What is the process to solve $$\frac{1 - \tan^2x}{1 + \tan^2x} = 0$$ ?

Set the numerator equal to zero: $$1 - \tan^2x = 0$$ .

What is the general solution for $$\tan x = k$$ ?

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

What is the significance of the unit circle in trigonometry?

The unit circle helps define the sine and cosine functions as the y and x coordinates of points on the circle.

What is the formula for the sine of a sum of angles?

The formula is $$\text{sin}(a + b) = \text{sin}a \text{cos}b + \text{cos}a \text{sin}b$$ .

What is the formula for the cosine of a sum of angles?

The formula is $$\text{cos}(a + b) = \text{cos}a \text{cos}b - \text{sin}a \text{sin}b$$ .

What is the first step in solving $$2\text{cos}^2x - 3\text{cos}x = 0$$ ?

Factor the equation: $$\text{cos}x(2\text{cos}x - 3) = 0$$ .

What is the solution set for $$\text{sin}x = 0$$ in the interval [0, 2π)?

The solution set is $$x = \text{0, π}$$ .

What is the process to solve $$1 - \text{sin}^2x + \text{sin}x = 1$$ ?

Set the equation equal to zero and factor out the GCF.

U7L3: Solving Trig Equations Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the range of the sine function?

Back

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

2.

FLASHCARD QUESTION

Front

What is the range of the cosine function?

Back

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

3.

FLASHCARD QUESTION

Front

What is the Pythagorean identity for sine and cosine?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What does it mean to set an equation equal to zero?

Back

Setting an equation equal to zero is a common step in solving equations, allowing for factoring or applying the zero product property.

7.

FLASHCARD QUESTION

Front

What is the zero product property?

Back

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