Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
[tex]\displaystyle \sin(2\theta)=\frac{2\sqrt{418}}{49}\approx0.8345[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos(\theta)=\frac{\sqrt{11}}{7}[/tex]
Where θ is in QI.
And we want to determine sin(2θ).
First, note that since θ is in QI, all trig ratios will be positive.
Next, recall that cosine is the ratio of the adjacent side to the hypotenuse. Therefore, the adjacent side a = √(11) and the hypotenuse c = 7.
Then by the Pythagorean Theorem, the opposite side to θ is:
[tex]b=\sqrt{(7)^2-(\sqrt{11})^2}=\sqrt{49-11}=\sqrt{38}[/tex]
So, with respect to θ, the adjacent side is √(11), the opposite side is √(38), and the hypotenuse is 7.
We can rewrite as expression as:
[tex]\sin(2\theta)=2\sin(\theta)\cos(\theta)[/tex]
Using the above information, substitute. Remember that all ratios will be positive:
[tex]\displaystyle =2\Big(\frac{\sqrt{38}}{7}\Big)\Big(\frac{\sqrt{11}}{7}\Big)[/tex]
Simplify. Therefore:
[tex]\displaystyle \sin(2\theta)=\frac{2\sqrt{418}}{49}\approx0.8345[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.