How do you find vertical asymptotes for the function $$f(x)=\frac{x^3-x^2-12x}{-2x^2+2x+4}$$ ?

To find vertical asymptotes, set the denominator equal to zero: $$-2x^2 + 2x + 4 = 0$$ . Solve for x to find the vertical asymptotes.

Given $$\tan\theta=-\sqrt{5}$$ and $$\sin\theta

Use the identity $$\tan\theta = \frac{\sin\theta}{\cos\theta}$$ . Since $$\tan\theta

How do you find the reference angle for $$\frac{7\pi}{6}$$ ?

The reference angle is found by subtracting $$\pi$$ from $$\frac{7\pi}{6}$$ : $$\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}$$ .

What is the period of $$y=8\cos(3\theta+\frac{\pi}{2})$$ ?

The period is $$\frac{2\pi}{3}$$ because $$B=3$$ .

How do you solve the equation $$\frac{8}{3}=\frac{1}{3}\tan(3\theta)+3$$ ?

First, isolate $$\tan(3\theta)$$ : $$\tan(3\theta) = 8 - 9 = -1$$ . Then, find the angles that satisfy this equation within the interval $$[0, 2\pi)$$ .

What are the solutions to $$\tan(3\theta) = -1$$ in the interval $$[0, 2\pi)$$ ?

The solutions are $$\frac{\pi}{4}, \frac{7\pi}{12}, \frac{11\pi}{12}, \frac{5\pi}{4}, \frac{19\pi}{12}, \frac{23\pi}{12}$$ .

What is the definition of a tangent function?

The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle, or as $$\tan\theta = \frac{\sin\theta}{\cos\theta}$$ .

What is the relationship between sine, cosine, and tangent?

The relationship is given by the identity: $$\tan\theta = \frac{\sin\theta}{\cos\theta}$$ .

How do you determine the sign of sine and cosine in different quadrants?

In Quadrant I, both sine and cosine are positive. In Quadrant II, sine is positive and cosine is negative. In Quadrant III, both are negative. In Quadrant IV, sine is negative and cosine is positive.

What is the significance of the unit circle in trigonometry?

The unit circle helps define the values of sine, cosine, and tangent for all angles, providing a visual representation of these functions and their periodic nature.

What is the formula for converting radians to degrees?

To convert radians to degrees, use the formula: $$\text{Degrees} = \text{Radians} \times \frac{180}{\pi}$$ .

What is the formula for converting degrees to radians?

To convert degrees to radians, use the formula: $$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$$ .

Fall Final Review #2 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where a function's value becomes infinite, typically at points where the denominator of a rational function equals zero.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is a reference angle?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the period of a cosine function?

Back

7.

FLASHCARD QUESTION

Front

Back

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