What is the general solution for the equation $$\tan(\theta) = k$$ ?

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

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

To solve, find the angle(s) where $$\text{sin}(\theta) = \frac{1}{2}$$ , which are $$\theta = \frac{\text{\text{pi}}}{6} + 2n\text{\text{pi}}$$ and $$\theta = \frac{5\text{\text{pi}}}{6} + 2n\text{\text{pi}}$$ .

What are the values of $$\text{sin}(\theta)$$ and $$\text{cos}(\theta)$$ at $$\theta = 0$$ ?

$$\text{sin}(0) = 0$$ and $$\text{cos}(0) = 1$$ .

How do you find the solutions for $$\text{cos}(\theta) = 0$$ in the interval $$[0, 2\text{pi})$$ ?

The solutions are $$\theta = \frac{\text{pi}}{2}$$ and $$\theta = \frac{3\text{pi}}{2}$$ .

What is the period of the sine function?

The period of the sine function is $$2\text{pi}$$ .

What is the difference between the sine and cosine functions?

Sine and cosine are both periodic functions, but sine represents the y-coordinate of a point on the unit circle, while cosine represents the x-coordinate.

How do you solve $$\text{sin}(\theta) = -\frac{1}{2}$$ for $$0 \text{ to } 2\text{pi}$$ ?

The solutions are $$\theta = \frac{7\text{pi}}{6}$$ and $$\theta = \frac{11\text{pi}}{6}$$ .

What is the cotangent function?

The cotangent function is the reciprocal of the tangent function, defined as $$\text{cot}(\theta) = \frac{\text{cos}(\theta)}{\text{sin}(\theta)}$$ .

What is the relationship between the angles in a right triangle and trigonometric functions?

In a right triangle, the sine, cosine, and tangent functions relate the angles to the ratios of the lengths of the sides.

How do you solve $$\text{tan}(\theta) = 1$$ for $$0 \text{ to } 2\text{pi}$$ ?

The solutions are $$\theta = \frac{\text{pi}}{4}$$ and $$\theta = \frac{5\text{pi}}{4}$$ .

What is the significance of the angle $$\frac{\text{pi}}{2}$$ in trigonometry?

The angle $$\frac{\text{pi}}{2}$$ (90 degrees) corresponds to the maximum value of the sine function and the minimum value of the cosine function.

Lesson 17 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, such as sine, cosine, or tangent.

Tags

CCSS.HSF.TF.B.7

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

4.

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

5.

FLASHCARD QUESTION

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane, used to define trigonometric functions.

Tags

CCSS.HSF.TF.A.2

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.2

7.

FLASHCARD QUESTION

Front

What is the Pythagorean identity?

Back

Tags

CCSS.HSF.TF.C.8

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