Question

The terminal side of θ passes through the point (−3,7). What is the exact value of sinθ in simplified form?

Answer 1

Answer: Exact value of sinθ  in simplified form is 66.8° .

Step-by-step explanation:

Since we have given that

(-3,7)=(x,y)

As the terminal side of f θ passes through the point (−3,7)

So, Perpendicular will be =7 units

Base = 3 units

Since we know that

$\sin \theta=\frac{Perpendicular}{Hypotenuse}\\\\\sin \theta=\frac{y}{\sqrt{x^+y^2}}\\\\\sin \theta=\frac{7}{\sqrt{9-3)^2+7^2}}\\\\\sin \theta=\frac{7}{\sqrt{9+49}}\\\\\sin \theta=\frac{7}{\sqrt{58}}\\\\\sin \theta=0.919\\\\\theta=\sin^{-1}(0.919)\\\\\theta=66.8\textdegree$

Hence, exact value of sinθ  in simplified form is 66.8° .