Question
upstudy study bank question image url

Which of the following statements shows how to calculate the reference angle for \( \theta=\frac{11 \pi}{6} \) ? \( \begin{array}{l}\pi-\theta \\ \theta-\pi \\ 2 \pi-\theta \\ \text { DONE }\end{array} \)

Ask by Joseph Elliott. in the United States
Feb 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The reference angle is calculated as \( 2\pi - \theta \).

Solution

To find the reference angle for an angle, we determine the acute angle that the terminal side makes with the x-axis. Since θ = 11π/6 is in the fourth quadrant, we use the formula for angles in the fourth quadrant:   Reference angle = 2π - θ Substituting:   Reference angle = 2π - 11π/6 = (12π/6 - 11π/6) = π/6 Thus, the correct statement is 2π - θ.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

To find the reference angle for \( \theta = \frac{11 \pi}{6} \), it's important to note that this angle lies in the fourth quadrant. The reference angle is determined by subtracting the angle from \( 2\pi \) since it is greater than \( \pi \). Thus, we calculate it using the formula \( 2\pi - \theta = 2\pi - \frac{11\pi}{6} = \frac{\pi}{6} \). A common mistake when calculating reference angles is to confuse the quadrants and apply the wrong formulas. Remember, angles in the first quadrant simply retain their value, angles in the second quadrant use \( \pi - \theta \), in the third quadrant it's \( \theta - \pi \), and in the fourth quadrant, like here, it's \( 2\pi - \theta \). Stay sharp with those quadrant rules!

Related Questions

Latest Trigonometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy