Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the reference angle for a rotation of (13 pi)/(12). Answer:

Find the reference angle for a rotation of 13π12 \frac{13 \pi}{12} .\newlineAnswer:\newline

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Inverses of csc, sec, and cotright chevron icon

Full solution

Q. Find the reference angle for a rotation of 13π12 \frac{13 \pi}{12} .\newlineAnswer:\newline
  1. Understand Reference Angles: First, we need to understand what a reference angle is. A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. It is always between 00 and π/2\pi/2 radians (or 00 and 9090 degrees) and is found by considering the angle's location relative to the nearest x-axis.
  2. Determine Angle Location: To find the reference angle for (13π/12)(13\pi/12) radians, we need to determine where this angle lies on the unit circle. Since π\pi radians is equivalent to 180180 degrees, (13π/12)(13\pi/12) radians is more than π\pi but less than 3π/23\pi/2 radians (or 180180 degrees but less than 270270 degrees), which places it in the third quadrant.
  3. Calculate Reference Angle: In the third quadrant, the reference angle is found by subtracting the angle from π\pi (or 180180 degrees). So, we calculate the reference angle as π−(13π12)\pi - (\frac{13\pi}{12}).
  4. Perform Subtraction: Perform the subtraction to find the reference angle: Reference angle = π−13π12=12π12−13π12=−π12\pi - \frac{13\pi}{12} = \frac{12\pi}{12} - \frac{13\pi}{12} = -\frac{\pi}{12}. Since a reference angle must be positive, we take the absolute value to get π12\frac{\pi}{12} radians.
  5. Correct Mistake: However, we made a mistake in the previous step. The angle (13π/12)(13\pi/12) is more than π\pi, so we should have subtracted it from 2π2\pi to find the reference angle in the third quadrant. Let's correct this:\newlineReference angle = 2π−(13π/12)=(24π/12)−(13π/12)=11π/122\pi - (13\pi/12) = (24\pi/12) - (13\pi/12) = 11\pi/12 radians.

More problems from Inverses of csc, sec, and cot

Question
Find all solutions with 0∘≤θ≤180∘0^\circ \leq \theta \leq 180^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecos⁡(θ)=−1\cos(\theta) = -1\newline‾∘\underline{\hspace{2em}}^\circ
Get tutor helpright-arrow

Posted 1 month ago

Question
Kimi's school is 1515 kilometers west of her house and 88 kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?\newline_____\_\_\_\_\_ kilometers
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.\newlinecos⁡35∘=\cos 35^\circ = __
Get tutor helpright-arrow

Posted 1 month ago

Question
Find all solutions with −90∘≤θ≤90∘-90^\circ \leq \theta \leq 90^\circ. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.\newlinecsc⁡(θ)=−1\csc(\theta) = -1\newline____ ∘\_\_\_\_\,^\circ
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecot⁡30∘=\cot 30^\circ = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
The terminal side of an angle θ\theta in standard position intersects the unit circle at (8485,1385)(\frac{84}{85}, \frac{13}{85}). What is cos⁡(θ)\cos(\theta)?\newlineWrite your answer in simplified, rationalized form.\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
−90∘<θ<90∘-90^\circ < \theta < 90^\circ. Find the value of θ\theta in degrees.\newlinetan⁡(θ)=0\tan(\theta) = 0\newlineWrite your answer in simplified, rationalized form. Do not round.\newlineθ=\theta = ____∘^\circ\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecsc⁡60∘=\csc 60^\circ = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.\newlinecos⁡90∘=\cos 90^\circ = ____
Get tutor helpright-arrow

Posted 2 months ago

View all (30)