Sketch a 251°25' ray on a Cartesian coordinate system and from a point on the ray sketch a right triangle. Label the sides of the triangle + or − . Determine the reference angle and the sine, cosine, tangent, cotangent, secant, and cosecant functions for the angle. Round the answers to 5 decimal places.

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Answer 1

Textbook Question

Chapter 72, Problem 1A

Sketch a 251°25' ray on a Cartesian coordinate system and from a point on the ray sketch a right triangle. Label the sides of the triangle $+$ or $−$ . Determine the reference angle and the sine, cosine, tangent, cotangent, secant, and cosecant functions for the angle. Round the answers to 5 decimal places.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Expert Solution & Answer

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

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Answer 2

Textbook Question

Chapter 72, Problem 1A

Sketch a 251°25' ray on a Cartesian coordinate system and from a point on the ray sketch a right triangle. Label the sides of the triangle $+$ or $−$ . Determine the reference angle and the sine, cosine, tangent, cotangent, secant, and cosecant functions for the angle. Round the answers to 5 decimal places.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Expert Solution & Answer

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

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Answer 3

Textbook Question

Chapter 72, Problem 1A

Sketch a 251°25' ray on a Cartesian coordinate system and from a point on the ray sketch a right triangle. Label the sides of the triangle $+$ or $−$ . Determine the reference angle and the sine, cosine, tangent, cotangent, secant, and cosecant functions for the angle. Round the answers to 5 decimal places.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Expert Solution & Answer

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

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Answer 4

Textbook Question

Chapter 72, Problem 1A

Sketch a 251°25' ray on a Cartesian coordinate system and from a point on the ray sketch a right triangle. Label the sides of the triangle $+$ or $−$ . Determine the reference angle and the sine, cosine, tangent, cotangent, secant, and cosecant functions for the angle. Round the answers to 5 decimal places.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Expert Solution & Answer

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Answer 8

Expert Solution & Answer

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

A ray of $251°25′$ , a right triangle from the ray, sine, cosine, tangent, cotangent, cosecant and secant.

Answer 12

Answer to Problem 1A

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Answer 13

Explanation of Solution

Given:

A ray of angle $220°10′$ .

Construction:

Take a Cartesian plane and draw a ray of angle $251°25′$ .
Draw a right triangle from the point of the ray.
Take negative sign on both base and height.

The sketch is shown below:

Mathematics For Machine Technology, Chapter 72, Problem 1A

Figure 1.

Calculation:

All the trigonometry functions are calculated as follows:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Conclusion:

The sketch is shown in Figure 1 and all the trigonometry values are given below:

$sin251°25′=−0.94786$

$cos251°25′=−0.31868$

$tan251°25′=2.97430$

$cot251°25′=0.33621$

$cosec251°25′=−1.05501$

$sec251°25′=−3.13791$

Answer 14

Ch. 72 - Sketch a 25125' ray on a Cartesian coordinate...Ch. 72 - Prob. 2A Ch. 72 - Prob. 3A Ch. 72 - Prob. 4A Ch. 72 - Prob. 5A Ch. 72 - Prob. 6A Ch. 72 - Prob. 7A Ch. 72 - Solve the following exercises using the Law of...Ch. 72 - Prob. 9A Ch. 72 - Find side x. All dimensions are in millimeters.

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