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:

If the angle theta=-(3pi)/(4) is in standard position on the unit circle, what ordered pair does its terminal side pass through?

If the angle θ=−3π4 \theta=-\frac{3 \pi}{4} is in standard position on the unit circle, what ordered pair does its terminal side pass through?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Find trigonometric ratios using the unit circleright chevron icon

Full solution

Q. If the angle θ=−3π4 \theta=-\frac{3 \pi}{4} is in standard position on the unit circle, what ordered pair does its terminal side pass through?
  1. Position on Unit Circle: Understand the position of the angle on the unit circle. The angle θ=−3π4\theta=-\frac{3\pi}{4} is in the third quadrant of the unit circle because it is negative and its absolute value is greater than π2\frac{\pi}{2} but less than π\pi.
  2. Reference Angle Determination: Determine the reference angle for θ=−3π4\theta=-\frac{3\pi}{4}.\newlineThe reference angle is the acute angle that the terminal side of θ\theta makes with the x-axis. Since θ\theta is in the third quadrant, its reference angle is π−∣θ∣=π−3π4=π4\pi - |\theta| = \pi - \frac{3\pi}{4} = \frac{\pi}{4}.
  3. Coordinates for Reference Angle: Find the coordinates for the reference angle π/4\pi/4 on the unit circle.\newlineFor the reference angle π/4\pi/4, the coordinates on the unit circle are (2/2,2/2)(\sqrt{2}/2, \sqrt{2}/2) because the unit circle has a radius of 11, and these are the xx and yy values for that angle in the first quadrant.
  4. Adjusting Coordinates: Adjust the coordinates for the third quadrant.\newlineSince θ=−3π4\theta=-\frac{3\pi}{4} is in the third quadrant, both the xx and yy coordinates will be negative. Therefore, the coordinates for θ=−3π4\theta=-\frac{3\pi}{4} are (−2/2,−2/2)(-\sqrt{2}/2, -\sqrt{2}/2).

More problems from Find trigonometric ratios using the unit circle

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 2 months 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 2 months 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 2 months 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 2 months ago

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

Posted 2 months 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 2 months 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 2 months 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 2 months ago

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

Posted 3 months ago

View all (5)