The function $$g$$ is given by $$g(x) = \tan\left(\frac{x}{3}\right) + 2$$ . Which of the following statements about $$g$$ is true?

(C) The period of $$g$$ is $$3\pi$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{3\pi}{2}+3\pi k$$ , where $$k$$ is an integer.

(A) The period of $$g$$ is $$\pi/3$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{\pi}{6}+\frac{\pi}{3}k$$ , where $$k$$ is an integer.

(B) The period of $$g$$ is $$\pi/3$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{\pi}{3}+\pi k$$ , where $$k$$ is an integer.

(D) The period of $$g$$ is $$3\pi$$ , and the graph of $$g$$ has vertical asymptotes where $$x=\frac{\pi}{2}+3\pi k$$ , where $$k$$ is an integer.

Find all solutions that satisfy the given equation: cos(x) = 1/2

x = π/3 + 2πk and x = 5π/3 + 2πk, where k is any integer

x = π/6 + 2πk and x = 11π/6 + 2πk, where k is any integer

x = π/3 + πk and x = 5π/3 + πk, where k is any integer

x = π/6 + πk and x = 11π/6 + πk, where k is any integer

Find all solutions that satisfy the given equation: sin(x) = 1/2

x = π/6 + 2πk and x = 5π/6 + 2πk, where k is any integer

x = π/3 + 2πk and x = 2π/3 + 2πk, where k is any integer

x = π/6 + πk and x = 5π/6 + πk, where k is any integer

x = π/3 + πk and x = 2π/3 + πk, where k is any integer

Find all solutions that satisfy the given equation: tan(x) = $$-\sqrt[]{3}$$

x = 2π/3 + πk, where k is any integer

x = π/6 + 2πk, where k is any integer

x = π/3 + πk, where k is any integer

x = π/6 + πk, where k is any integer

Which of the following represents all values of θ, 0 ≤ θ < 2π satisfying cosθ > 1/2?

0 < θ < π/3 and 5π/3 < θ < 2π

Study Guide: Topics 3.8-3.10

Authored by Isabel Ibarra

Mathematics

12th Grade

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

√2

1/√2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-1

undefined

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

-1/√3

1/√3

√3

-√3

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

π/3

π/2

2π

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph of the function g is shown in the xy-plane. Which of the following statements is true?

For 0 < x < 2π, the graph of g is increasing at an increasing rate.

For 0 < x < 2π, the graph of g is increasing at a decreasing rate.

For 0 < x < 2π, the graph of g is decreasing at an increasing rate.

For 0 < x < 2π, the graph of g is decreasing at a decreasing rate.

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Study Guide: Topics 3.8-3.10

The graph of the function g is shown in the xy-plane. Which of the following statements is true?

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