Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For which values is tanθ\tan \theta positive? \newlineA. all radian values between 00 and π\pi \newlineB. all radian values between π4\frac{\pi}{4} and 3π4\frac{3\pi}{4} \newlineC. all radian values between π2\frac{\pi}{2} and π\pi \newlineD. all radian values between π\pi and 3π2\frac{3\pi}{2}

Full solution

Q. For which values is tanθ\tan \theta positive? \newlineA. all radian values between 00 and π\pi \newlineB. all radian values between π4\frac{\pi}{4} and 3π4\frac{3\pi}{4} \newlineC. all radian values between π2\frac{\pi}{2} and π\pi \newlineD. all radian values between π\pi and 3π2\frac{3\pi}{2}
  1. Understand tan(θ)\tan(\theta): Understand the trigonometric function tan(θ)\tan(\theta). tan(θ)\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).
  2. Determine first quadrant radians: Determine the radian values for the first quadrant. The first quadrant is from 00 to π2\frac{\pi}{2} radians.
  3. Determine third quadrant radians: Determine the radian values for the third quadrant. The third quadrant is from π\pi to 3π2\frac{3\pi}{2} radians.
  4. Combine information for positive tan(θ)\tan(\theta): Combine the information from steps 22 and 33 to find the range of radian values where tan(θ)\tan(\theta) is positive. tan(θ)\tan(\theta) is positive between 00 and π2\frac{\pi}{2} radians and between π\pi and 3π2\frac{3\pi}{2} radians.
  5. Match range to options: Match the combined range from step 44 to the given options. The correct option that includes all the radian values where tan(θ)\tan(\theta) is positive is (D) all radian values between π\pi and 3π2\frac{3\pi}{2}.

More problems from Convert between radians and degrees