Question

I am not even sure what ϕ is, can you help me solve?

Answer 1

Answer:

$-\frac{1}{17\sqrt5}$

Step-by-step explanation:

You do not require the value of  $\phi$  (which is just a symbol to denote a variable like $\theta$) to solve the question.

Recall the formula: $\sin(\theta +\phi)=\sin{\theta}\cos{\phi}+\sin{\phi}\cos{\theta}$

Now using the given values you can find the rest of required.

$\cos{\theta}=\frac{\sqrt{17^2-8^2}}{17}=\frac{15}{17}$

$\sin{\phi} = \frac{\sqrt{5^2-(2\sqrt5)^2}}{5}=\frac{1}{\sqrt5}$

Now just plug in the values in the formula.

$\sin{(\theta + \phi)} = \frac{8}{17}\left(- \frac{2}{\sqrt5} \right)+\frac{15}{17}\frac{1}{\sqrt5}\\=-\frac{1}{17\sqrt5}$

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