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

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

How do you solve the equation $$\tan x = 0$$ ?

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

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

The solutions are $$x = \frac{\text{pi}}{6} + 2n\text{pi}$$ and $$x = \frac{5\text{pi}}{6} + 2n\text{pi}$$ , where n is any integer.

What is the formula for converting between degrees and radians?

To convert degrees to radians, multiply by $$\frac{\text{pi}}{180}$$ . To convert radians to degrees, multiply by $$\frac{180}{\text{pi}}$$ .

Define the term 'trigonometric equation'.

A trigonometric equation is an equation that involves trigonometric functions of a variable.

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

The solutions are $$x = \frac{\text{pi}}{2} + n\text{pi}$$ , where n is any integer.

How do you solve the equation $$2\text{sin} x + 1 = 0$$ ?

The solution is $$x = \frac{7\text{pi}}{6}, \frac{11\text{pi}}{6}$$ in the interval $$(0, 2\text{pi}]$$ .

What is the significance of the unit circle in trigonometry?

The unit circle allows us to define trigonometric functions for all angles and provides a geometric interpretation of these functions.

What is the double angle formula for sine?

The double angle formula for sine is $$\text{sin}(2x) = 2\text{sin}(x)\text{cos}(x)$$ .

What is the relationship between sine and cosine for complementary angles?

For complementary angles, $$\text{sin}(x) = \text{cos}(\frac{\text{pi}}{2} - x)$$ .

Solving Trigonometric Equations Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Define the sine function in terms of a right triangle.

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

2.

FLASHCARD QUESTION

Front

What is the cosine function and how is it defined?

Back

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Tags

CCSS.HSG.SRT.C.6

3.

FLASHCARD QUESTION

Front

State the Pythagorean identity involving sine and cosine.

Back

Tags

CCSS.HSF.TF.C.8

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 range of the sine function?

Back

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

Tags

CCSS.HSF.TF.A.4

7.

FLASHCARD QUESTION

Front

What is the range of the cosine function?

Back

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

Tags

CCSS.HSF.TF.A.4

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