Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine the value of [tex]\(\tan 45^{\circ}\)[/tex], we need to evaluate the trigonometric function tangent for the angle of 45 degrees.
1. Recognize the angle and its position:
- The angle [tex]\(45^{\circ}\)[/tex] is in the first quadrant, where all trigonometric functions are positive.
2. Understand the properties of tangent:
- The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.
- For a [tex]\(45^{\circ}\)[/tex] angle in a right triangle, both the opposite and adjacent sides are equal. Hence, their ratio is 1.
3. Evaluate [tex]\(\tan 45^{\circ}\)[/tex]:
- Since [tex]\(\tan 45^{\circ}\)[/tex] is the ratio of two equal sides, this gives [tex]\(\tan 45^{\circ} = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{1} = 1\)[/tex].
4. Answer:
- Therefore, [tex]\(\tan 45^{\circ} = 1\)[/tex].
Given the options:
A. [tex]\(\frac{1}{2}\)[/tex]
B. [tex]\(\sqrt{2}\)[/tex]
C. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
D. 1
The correct answer is:
D. 1.
1. Recognize the angle and its position:
- The angle [tex]\(45^{\circ}\)[/tex] is in the first quadrant, where all trigonometric functions are positive.
2. Understand the properties of tangent:
- The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.
- For a [tex]\(45^{\circ}\)[/tex] angle in a right triangle, both the opposite and adjacent sides are equal. Hence, their ratio is 1.
3. Evaluate [tex]\(\tan 45^{\circ}\)[/tex]:
- Since [tex]\(\tan 45^{\circ}\)[/tex] is the ratio of two equal sides, this gives [tex]\(\tan 45^{\circ} = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{1} = 1\)[/tex].
4. Answer:
- Therefore, [tex]\(\tan 45^{\circ} = 1\)[/tex].
Given the options:
A. [tex]\(\frac{1}{2}\)[/tex]
B. [tex]\(\sqrt{2}\)[/tex]
C. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
D. 1
The correct answer is:
D. 1.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.