Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given the reference angle of
(3pi)/(8), find the corresponding angle in Quadrant 3.
Answer:

Given the reference angle of $\frac{3 \pi}{8}$ , find the corresponding angle in Quadrant $3$ . $\newline$ Answer:

View step-by-step help

View step-by-step help

Full solution

Q. Given the reference angle of

\frac{3 \pi}{8}

, find the corresponding angle in Quadrant

3

.

\newline

Answer:

Concept Explanation: Understand the concept of reference angles and quadrants. $\newline$ A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. Quadrant $3$ is where both $x$ and $y$ coordinates are negative. To find the corresponding angle in Quadrant $3$ , we need to add $\pi$ to the reference angle because angles in Quadrant $3$ are between $\pi$ and $\frac{3\pi}{2}$ .
Calculate Angle: Calculate the corresponding angle in Quadrant $3$ . The reference angle is $(3\pi)/(8)$ . To find the corresponding angle in Quadrant $3$ , we add $\pi$ to the reference angle: $(3\pi)/(8) + \pi$ .
Simplify Expression: Simplify the expression. $\newline$ To add the angles, we need a common denominator. Since $\pi$ is the same as $(8\pi)/(8)$ , we can write the sum as: $(3\pi)/(8) + (8\pi)/(8) = (11\pi)/(8)$ .
Verify Quadrant: Verify that the resulting angle is indeed in Quadrant $3$ . The angle $(11\pi)/(8)$ is greater than $\pi$ and less than $3\pi/2$ , which confirms that it is in Quadrant $3$ .

More problems from Quadrants

Question

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\cos(\theta) = -1

\newline

\underline{\hspace{2em}}^\circ

Posted 1 month ago

Question

Kimi's school is

15

kilometers west of her house and

8

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

\_\_\_\_\_

Posted 1 month ago

Question

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

\newline

\cos 35^\circ =

Posted 1 month ago

Question

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

\newline

\_\_\_\_\,^\circ

Posted 1 month ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cot 30^\circ =

Posted 1 month ago

Question

The terminal side of an angle

\theta

in standard position intersects the unit circle at

(\frac{84}{85}, \frac{13}{85})

\cos(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

Posted 1 month ago

Question

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

^\circ

\newline

Posted 2 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

Posted 1 month ago

Question

\theta

is an acute angle. Find the value of

\theta

\newline

\sec(\theta) = \sqrt{2}

\newline

\theta =

\degree

Posted 1 month ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cos 90^\circ =

Posted 2 months ago