Discover the best answers to your questions with the help of IDNLearn.com. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.
Sagot :
To solve the problem where [tex]\(\tan \theta = \sqrt{3}\)[/tex] and [tex]\(\theta\)[/tex] is an acute angle, we need to find the value of [tex]\(1 + \cos \theta\)[/tex]. Here is the detailed step-by-step solution:
1. Identify the angle [tex]\(\theta\)[/tex]:
Since [tex]\(\tan \theta = \sqrt{3}\)[/tex] and [tex]\(\theta\)[/tex] is an acute angle, we can recognize that [tex]\(\theta = 60^\circ\)[/tex] because [tex]\(\tan 60^\circ = \sqrt{3}\)[/tex].
2. Determine [tex]\(\cos \theta\)[/tex]:
Once we know [tex]\(\theta = 60^\circ\)[/tex], we can find [tex]\(\cos \theta\)[/tex]. From trigonometric ratios, we know that:
[tex]\[ \cos 60^\circ = \frac{1}{2} \][/tex]
3. Calculate [tex]\(1 + \cos \theta\)[/tex]:
Substitute the value of [tex]\(\cos \theta\)[/tex]:
[tex]\[ 1 + \cos 60^\circ = 1 + \frac{1}{2} \][/tex]
4. Simplify the expression:
[tex]\[ 1 + \frac{1}{2} = 1 + 0.5 = 1.5 \][/tex]
Therefore, the value of [tex]\(1 + \cos \theta\)[/tex] is [tex]\(1.5\)[/tex].
1. Identify the angle [tex]\(\theta\)[/tex]:
Since [tex]\(\tan \theta = \sqrt{3}\)[/tex] and [tex]\(\theta\)[/tex] is an acute angle, we can recognize that [tex]\(\theta = 60^\circ\)[/tex] because [tex]\(\tan 60^\circ = \sqrt{3}\)[/tex].
2. Determine [tex]\(\cos \theta\)[/tex]:
Once we know [tex]\(\theta = 60^\circ\)[/tex], we can find [tex]\(\cos \theta\)[/tex]. From trigonometric ratios, we know that:
[tex]\[ \cos 60^\circ = \frac{1}{2} \][/tex]
3. Calculate [tex]\(1 + \cos \theta\)[/tex]:
Substitute the value of [tex]\(\cos \theta\)[/tex]:
[tex]\[ 1 + \cos 60^\circ = 1 + \frac{1}{2} \][/tex]
4. Simplify the expression:
[tex]\[ 1 + \frac{1}{2} = 1 + 0.5 = 1.5 \][/tex]
Therefore, the value of [tex]\(1 + \cos \theta\)[/tex] is [tex]\(1.5\)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Accurate answers are just a click away at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.