At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine which equation correctly solves for [tex]\(\theta\)[/tex], we'll examine the mathematical operations and functions typically used to determine angles in trigonometry.
1. [tex]\(\theta = \sin^{-1}\left(\frac{4}{13}\right)\)[/tex]
2. [tex]\(\theta = \tan\left(\frac{4}{13}\right)\)[/tex]
3. [tex]\(\theta = \sin\left(\frac{4}{13}\right)\)[/tex]
4. [tex]\(\theta = \tan^{-1}\left(\frac{4}{13}\right)\)[/tex]
Step-by-step Explanation:
1. [tex]\(\theta = \sin^{-1}\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\sin^{-1}(x)\)[/tex] is the inverse sine function, often called arcsine. It solves for the angle [tex]\(\theta\)[/tex] such that [tex]\(\sin(\theta) = x\)[/tex].
- Here, [tex]\( \theta = \sin^{-1}\left(\frac{4}{13}\right) \)[/tex] would mean [tex]\(\sin(\theta) = \frac{4}{13}\)[/tex].
2. [tex]\(\theta = \tan\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\tan(x)\)[/tex] is the tangent function. It provides the ratio of the opposite side to the adjacent side for a given angle [tex]\(\theta\)[/tex].
- Here, [tex]\(\theta = \tan\left(\frac{4}{13}\right)\)[/tex] does not make sense because [tex]\(\tan\)[/tex] is not solving for [tex]\(\theta\)[/tex]; it's providing a ratio.
3. [tex]\(\theta = \sin\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\sin(x)\)[/tex] is the sine function. It calculates the ratio of the opposite side to the hypotenuse for a given angle [tex]\(\theta\)[/tex].
- Here, [tex]\(\theta = \sin\left(\frac{4}{13}\right)\)[/tex] does not make sense because [tex]\(\sin\)[/tex] is not solving for [tex]\(\theta\)[/tex]; it's calculating a ratio.
4. [tex]\(\theta = \tan^{-1}\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\tan^{-1}(x)\)[/tex] is the inverse tangent function, often called arctangent. It solves for the angle [tex]\(\theta\)[/tex] such that [tex]\(\tan(\theta) = x\)[/tex].
- Here, [tex]\(\theta = \tan^{-1}\left(\frac{4}{13}\right) \)[/tex] would mean [tex]\(\tan(\theta) = \frac{4}{13}\)[/tex].
Therefore, the equation that correctly solves for [tex]\(\theta\)[/tex] in this context is:
[tex]\[ \theta = \tan^{-1}\left(\frac{4}{13}\right) \][/tex]
The correct choice is:
[tex]\[ \boxed{\theta = \tan^{-1}\left(\frac{4}{13}\right)} \][/tex]
1. [tex]\(\theta = \sin^{-1}\left(\frac{4}{13}\right)\)[/tex]
2. [tex]\(\theta = \tan\left(\frac{4}{13}\right)\)[/tex]
3. [tex]\(\theta = \sin\left(\frac{4}{13}\right)\)[/tex]
4. [tex]\(\theta = \tan^{-1}\left(\frac{4}{13}\right)\)[/tex]
Step-by-step Explanation:
1. [tex]\(\theta = \sin^{-1}\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\sin^{-1}(x)\)[/tex] is the inverse sine function, often called arcsine. It solves for the angle [tex]\(\theta\)[/tex] such that [tex]\(\sin(\theta) = x\)[/tex].
- Here, [tex]\( \theta = \sin^{-1}\left(\frac{4}{13}\right) \)[/tex] would mean [tex]\(\sin(\theta) = \frac{4}{13}\)[/tex].
2. [tex]\(\theta = \tan\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\tan(x)\)[/tex] is the tangent function. It provides the ratio of the opposite side to the adjacent side for a given angle [tex]\(\theta\)[/tex].
- Here, [tex]\(\theta = \tan\left(\frac{4}{13}\right)\)[/tex] does not make sense because [tex]\(\tan\)[/tex] is not solving for [tex]\(\theta\)[/tex]; it's providing a ratio.
3. [tex]\(\theta = \sin\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\sin(x)\)[/tex] is the sine function. It calculates the ratio of the opposite side to the hypotenuse for a given angle [tex]\(\theta\)[/tex].
- Here, [tex]\(\theta = \sin\left(\frac{4}{13}\right)\)[/tex] does not make sense because [tex]\(\sin\)[/tex] is not solving for [tex]\(\theta\)[/tex]; it's calculating a ratio.
4. [tex]\(\theta = \tan^{-1}\left(\frac{4}{13}\right)\)[/tex]:
- The expression [tex]\(\tan^{-1}(x)\)[/tex] is the inverse tangent function, often called arctangent. It solves for the angle [tex]\(\theta\)[/tex] such that [tex]\(\tan(\theta) = x\)[/tex].
- Here, [tex]\(\theta = \tan^{-1}\left(\frac{4}{13}\right) \)[/tex] would mean [tex]\(\tan(\theta) = \frac{4}{13}\)[/tex].
Therefore, the equation that correctly solves for [tex]\(\theta\)[/tex] in this context is:
[tex]\[ \theta = \tan^{-1}\left(\frac{4}{13}\right) \][/tex]
The correct choice is:
[tex]\[ \boxed{\theta = \tan^{-1}\left(\frac{4}{13}\right)} \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
