Find the values of the trigonometric ratios from the graph ### Understanding the Unit CircleThe image depicts a unit circle, which is a fundamental concept in trigonometry and is often used to define sine, cosine, and tangent functions for all real numbers.#### Components of the Diagram:- **Circle:** The circle shown has a radius of 1 unit and is centered at the origin of the coordinate system (0, 0).- **Axes:** The horizontal and vertical lines represent the x-axis and y-axis, respectively.- **Point:** The point on the circumference of the circle is marked as $(-0.4, 0.917)$.- **Arrows and Curve:** The curved arrow indicates the direction in which the angle is measured from the positive x-axis, typically counterclockwise in standard position.#### Significance of Each Component:1. **Unit Circle and Coordinates:** - The unit circle helps in visualizing the trigonometric functions. - Any point $(x, y)$ on the circle satisfies the equation $x^2 + y^2 = 1$. - In this graph, the point $(-0.4, 0.917)$ indicates a position on the unit circle. The x-coordinate is -0.4, and the y-coordinate is 0.917.2. **Trigonometric Functions:** - For the point $(x, y)$ on the unit circle, $x$ represents the cosine of the angle, and $y$ represents the sine of the angle. - Here, $\cos(\theta) = -0.4$ and $\sin(\theta) = 0.917$, where $\theta$ is the angle formed with the positive x-axis.3. **Direction of Measurement:** - The arrow illustrates the direction in which the angle increases. Angles are typically measured counterclockwise from the positive x-axis. #### Application:Understanding the unit circle is critical for solving problems in trigonometry, particularly those involving periodic functions, wave functions, and oscillations. It provides a geometric representation of the trigonometric functions, making it easier to understand their properties and relationships.By studying the coordinates of various points on the unit circle, students can grasp the values of sine and cosine functions for angles in all four quadrants.For more detailed study, students should practice finding coordinates of specific angles and using them to evaluate trigonometric functions. ### Trigonometric Function ValuesUse the dropdown menus to select the appropriate values for the following trigonometric functions:1. $ \sin x = $ ____2. $ \cos x = $ ____3. $ \tan x = $ ____#### Select the appropriate value from the following options:- a. $-0.4$- b. $0.4$- c. $-2.293$- d. $-0.917$- e. $0.917$Make sure to review your choices carefully based on the context provided.

Name: Find the values of the trigonometric ratios from the graph ### Underst
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Find the values of the trigonometric ratios from the graph ### Understanding the Unit CircleThe image depicts a unit circle, which is a fundamental concept in trigonometry and is often used to define sine, cosine, and tangent functions for all real n

Answered: Find the values of the trigonometric…

Math

Trigonometry

Find the values of the trigonometric ratios from the graph

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

See similar textbooks

Related questions

Q: What is the relationship between mLABCand MLADC?

A: GivenCircle B with tangent AD and tangent DCArc AC has a measure of 85 degrees.Now here B is the…

Q: On a blank sheet of paper, use words and illustrations to describe the cosine function in the…

Q: Please show how to draw this on the quadrant.

A: Given:

Q: If you were tasked with collecting data that could follow a trigonometric function, describe your…

A: You can go on to track down the position of a pendulum (or any object that exhibits Simple Harmonic…

Q: Use the unit eircle to evaluate the six trigonometric functions of 0. 20. 450°

Q: Summarize the three core types of trigonometric ratios showing what each ratio is.

A: Solution

Q: Sketch the angle and write the sec and tan of the angle if the terminal side of the angle passes…

A: NOTE: Refresh your page if you can't see any equations. . the given point is so here we have

Q: Proove that the following equalities are true using trigonometric identities. 1. sinθ = tan2θ (1 -…

Q: Graph the point P (-5, -4) on the terminal arm of angle Theta, and determine the EXACT values of the…

A: The point is lies in 3rd quadrant

Q: The radius of the circle P rotates around is 1 meter: Priya is thinking about the windmill in an…

A: What do you think Priya means by rotating -π/2 radians ? Do you agree with Priya ?

Q: standard

A: please refer to the image below

Q: In building a tent, Jada ties a rope from the top of a pole 3 meters high to a stake that is 4…

Q: Why are the trigonometric functions sometimes called circular functions?

A: Trigonometric functions are called circular functions because function values can be expressed in…

Q: Explain, using the four quadrants of the unit circle, how to find in which quadrants sine, cosine,…

Q: Explain how to find all 6 trigonometric ratios if you are given secθ=2√3

A: Answer and explanation is given below

Q: Find the coordinates of the point on a circle with radius 16 corresponding to an angle of SHI If…

A: If you have any problem let me know here in comment box for this thankyou for your question.

Q: draw a triangle that represents this situation. Then, find the cosine and tangent ratios for 41…

A: sin E = 941⇒E = 12.71°

Q: how do i find the radius of 49 pi?

Q: Find the point on the Unit Circle associated with the angle 5pi/3

A: Given angle is To determine the point on the Unit Circle associated with the angle 5pi/3

Concept explainers

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

Topic Video

Question

100%

Find the values of the trigonometric ratios from the graph

### Understanding the Unit Circle

The image depicts a unit circle, which is a fundamental concept in trigonometry and is often used to define sine, cosine, and tangent functions for all real numbers.

#### Components of the Diagram:

- **Circle:** The circle shown has a radius of 1 unit and is centered at the origin of the coordinate system (0, 0).
- **Axes:** The horizontal and vertical lines represent the x-axis and y-axis, respectively.
- **Point:** The point on the circumference of the circle is marked as $(-0.4, 0.917)$.
- **Arrows and Curve:** The curved arrow indicates the direction in which the angle is measured from the positive x-axis, typically counterclockwise in standard position.

#### Significance of Each Component:

1. **Unit Circle and Coordinates:**
- The unit circle helps in visualizing the trigonometric functions.
- Any point $(x, y)$ on the circle satisfies the equation $x^2 + y^2 = 1$.
- In this graph, the point $(-0.4, 0.917)$ indicates a position on the unit circle. The x-coordinate is -0.4, and the y-coordinate is 0.917.

2. **Trigonometric Functions:**
- For the point $(x, y)$ on the unit circle, $x$ represents the cosine of the angle, and $y$ represents the sine of the angle.
- Here, $\cos(\theta) = -0.4$ and $\sin(\theta) = 0.917$, where $\theta$ is the angle formed with the positive x-axis.

3. **Direction of Measurement:**
- The arrow illustrates the direction in which the angle increases. Angles are typically measured counterclockwise from the positive x-axis.

#### Application:

Understanding the unit circle is critical for solving problems in trigonometry, particularly those involving periodic functions, wave functions, and oscillations. It provides a geometric representation of the trigonometric functions, making it easier to understand their properties and relationships.

By studying the coordinates of various points on the unit circle, students can grasp the values of sine and cosine functions for angles in all four quadrants.

For more detailed study, students should practice finding coordinates of specific angles and using them to evaluate trigonometric functions.

### Trigonometric Function Values

Use the dropdown menus to select the appropriate values for the following trigonometric functions:

1. $ \sin x = $ ____
2. $ \cos x = $ ____
3. $ \tan x = $ ____

#### Select the appropriate value from the following options:
- a. $-0.4$
- b. $0.4$
- c. $-2.293$
- d. $-0.917$
- e. $0.917$

Make sure to review your choices carefully based on the context provided.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamentals of Trigonometric Identities$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions

Write a short response to this statement, which is often used by one of the authors of this text in trigonometry classes: Students who tend to ignore negative signs should enjoy graphing functions involving the cosine and the secant.
Why are radians used more commonly in math modeling problems rather than degrees?
How should I explain this question?
DO NOT use the Sine Rule or Cosine Rule to answer this. Use right-angled triangle trigonometry only. A building casts a 20 meter shadow. The line between the top of the buiding and the end of the shadow makes an angle of π3 radians with the building. Find the height of the building correct to 2 decimal places. The height of the building is: metres.
Select one area of application of trigonometric ratios in engineering or architecture. Describe the kind of problem that can be solved in that area, as well as the general solution process. Use complete sentences.
Find the coordinates of the point on a circle with a radius of 8 corresponding to an angle 7pi/4. Then find sine and cosine of the angles.