Use a calculator to find the value of the trigonometric function to four decimal places. tan 3.7 Answers: 0.5298 0.0647 0.8481 0.6247
Use a calculator to find the value of the trigonometric function to four decimal places. tan 3.7 Answers: 0.5298 0.0647 0.8481 0.6247
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°.
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![### Trigonometric Functions: Determining Values Using a Calculator
To accurately determine the value of the tangent function for a given angle, we can use a scientific calculator. This process will involve finding the tangent of 3.7 radians and rounding the result to four decimal places.
**Problem Statement:**
Use a calculator to find the value of the trigonometric function to four decimal places.
\[ \tan(3.7) \]
**Possible Answers:**
1. 0.5298
2. 0.0647
3. 0.8481
4. 0.6247
### Detailed Steps on Using a Calculator:
1. Ensure your calculator is set to radian mode, as the angle given (3.7) is in radians.
2. Enter the value 3.7 into the calculator.
3. Use the trigonometric function button to calculate the tangent of 3.7.
4. Round the resulting value to four decimal places.
By following these steps, you should be able to identify the correct answer among the given options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F934f745f-cc11-47f6-819f-30e7adcd517f%2F84803e98-b89e-449d-aef1-bd151c0e4d7f%2Fmw2qgzjq.png&w=3840&q=75)
Transcribed Image Text:### Trigonometric Functions: Determining Values Using a Calculator
To accurately determine the value of the tangent function for a given angle, we can use a scientific calculator. This process will involve finding the tangent of 3.7 radians and rounding the result to four decimal places.
**Problem Statement:**
Use a calculator to find the value of the trigonometric function to four decimal places.
\[ \tan(3.7) \]
**Possible Answers:**
1. 0.5298
2. 0.0647
3. 0.8481
4. 0.6247
### Detailed Steps on Using a Calculator:
1. Ensure your calculator is set to radian mode, as the angle given (3.7) is in radians.
2. Enter the value 3.7 into the calculator.
3. Use the trigonometric function button to calculate the tangent of 3.7.
4. Round the resulting value to four decimal places.
By following these steps, you should be able to identify the correct answer among the given options.
![### Using the Pythagorean Theorem to Find the Length of the Missing Side and Trigonometric Functions
To solve a right triangle problem using the Pythagorean Theorem and to find the indicated trigonometric function, follow these steps:
#### Problem Statement
Find \( \sin \theta \).
#### Right Triangle Diagram
The triangle diagram is a right triangle with:
- \( AB = \text{Hypotenuse} \)
- \( BC = \text{Opposite side to } \theta \)
- \( CA = \text{Adjacent side to } \theta \)
Here,
- \( BC = 2 \)
- \( CA = 3 \)
#### Steps to Solve
1. **Find the length of the hypotenuse \( AB \)**:
Using the Pythagorean Theorem:
\[
AB^2 = BC^2 + CA^2
\]
\[
AB^2 = 2^2 + 3^2
\]
\[
AB^2 = 4 + 9
\]
\[
AB^2 = 13
\]
\[
AB = \sqrt{13}
\]
2. **Find \( \sin \theta \)**:
\[
\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AB}
\]
\[
\sin \theta = \frac{2}{\sqrt{13}}
\]
3. **Rationalize the Denominator**:
\[
\sin \theta = \frac{2}{\sqrt{13}} \times \frac{\sqrt{13}}{\sqrt{13}}
\]
\[
\sin \theta = \frac{2\sqrt{13}}{13}
\]
#### Answer Options
The possible answers provided are:
1. \( \frac{\sqrt{13}}{2} \)
2. \( \frac{3\sqrt{13}}{13} \)
3. \( \frac{2\sqrt{13}}{13} \)
4. \( \frac{\sqrt{13}}{3} \)
### Conclusion
The correct answer is:
\[ \frac{2\sqrt{13}}{13} \]
Use these steps to solve similar problems involving](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F934f745f-cc11-47f6-819f-30e7adcd517f%2F84803e98-b89e-449d-aef1-bd151c0e4d7f%2Fmi31tpe.png&w=3840&q=75)
Transcribed Image Text:### Using the Pythagorean Theorem to Find the Length of the Missing Side and Trigonometric Functions
To solve a right triangle problem using the Pythagorean Theorem and to find the indicated trigonometric function, follow these steps:
#### Problem Statement
Find \( \sin \theta \).
#### Right Triangle Diagram
The triangle diagram is a right triangle with:
- \( AB = \text{Hypotenuse} \)
- \( BC = \text{Opposite side to } \theta \)
- \( CA = \text{Adjacent side to } \theta \)
Here,
- \( BC = 2 \)
- \( CA = 3 \)
#### Steps to Solve
1. **Find the length of the hypotenuse \( AB \)**:
Using the Pythagorean Theorem:
\[
AB^2 = BC^2 + CA^2
\]
\[
AB^2 = 2^2 + 3^2
\]
\[
AB^2 = 4 + 9
\]
\[
AB^2 = 13
\]
\[
AB = \sqrt{13}
\]
2. **Find \( \sin \theta \)**:
\[
\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AB}
\]
\[
\sin \theta = \frac{2}{\sqrt{13}}
\]
3. **Rationalize the Denominator**:
\[
\sin \theta = \frac{2}{\sqrt{13}} \times \frac{\sqrt{13}}{\sqrt{13}}
\]
\[
\sin \theta = \frac{2\sqrt{13}}{13}
\]
#### Answer Options
The possible answers provided are:
1. \( \frac{\sqrt{13}}{2} \)
2. \( \frac{3\sqrt{13}}{13} \)
3. \( \frac{2\sqrt{13}}{13} \)
4. \( \frac{\sqrt{13}}{3} \)
### Conclusion
The correct answer is:
\[ \frac{2\sqrt{13}}{13} \]
Use these steps to solve similar problems involving
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