For which values is tan theta positive? A. all radian values between (0 and pi B. all radian values between (pi)/(4) and (3pi)/(4) c. all radian values between (pi)/(2) and pi (D) D. all radian values between pi and (3pi)/(2)

Understand tan(theta): Understand the trigonometric function tan(theta). Tan(theta) is positive in the first and third quadrants where both sine and cosine have the same sign (both positive in the first quadrant and both negative in the third quadrant).Determine first quadrant radians: Determine the radian values for the first quadrant. The first quadrant is from 0 to π/2 radians.Determine third quadrant radians: Determine the radian values for the third quadrant. The third quadrant is from π to 3π/2 radians.Combine information for positive tan(theta): Combine the information from steps 2 and 3 to find the range of radian values where tan(theta) is positive. Tan(theta) is positive between 0 and π/2 radians and between π and 3π/2 radians.Match range to options: Match the combined range from step 4 to the given options. The correct option that includes all the radian values where tan(theta) is positive is (D) all radian values between π and 3π/2.

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For which values is $\tan \theta$ positive? $\newline$ A. all radian values between $0$ and $\pi$ $\newline$ B. all radian values between $\frac{\pi}{4}$ and $\frac{3\pi}{4}$ $\newline$ C. all radian values between $\frac{\pi}{2}$ and $\pi$ $\newline$ D. all radian values between $\pi$ and $\frac{3\pi}{2}$

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Math Problems

Algebra 2

Convert between radians and degrees

Full solution

Q. For which values is

\tan \theta

positive?

\newline

A. all radian values between

0

and

\pi

\newline

B. all radian values between

\frac{\pi}{4}

and

\frac{3\pi}{4}

\newline

C. all radian values between

\frac{\pi}{2}

and

\pi

\newline

D. all radian values between

\pi

and

\frac{3\pi}{2}

Understand $\tan(\theta)$ : Understand the trigonometric function $\tan(\theta)$ . $\tan(\theta)$ is positive in the first and third quadrants where both sine and cosine have the same sign (both positive in the first quadrant and both negative in the third quadrant).
Determine first quadrant radians: Determine the radian values for the first quadrant. The first quadrant is from $0$ to $\frac{\pi}{2}$ radians.
Determine third quadrant radians: Determine the radian values for the third quadrant. The third quadrant is from $\pi$ to $\frac{3\pi}{2}$ radians.
Combine information for positive $\tan(\theta)$ : Combine the information from steps $2$ and $3$ to find the range of radian values where $\tan(\theta)$ is positive. $\tan(\theta)$ is positive between $0$ and $\frac{\pi}{2}$ radians and between $\pi$ and $\frac{3\pi}{2}$ radians.
Match range to options: Match the combined range from step $4$ to the given options. The correct option that includes all the radian values where $\tan(\theta)$ is positive is (D) all radian values between $\pi$ and $\frac{3\pi}{2}$ .