Question

What is the value of cos 0 given that (-2 , 9 ) is a point on the terminal side of 0 ?

Answer 1

Answer:

The third choice down

Step-by-step explanation:

Plotting the point (-2, 9) has us in QII.  We connect the point to the origin and then drop the altitude to the negative x-axis, creating a right triangle.  The side adjacent to the reference angle theta is |-2| and the alltitude (height) is 9.  The sin of the angle is found in the side opposite the angle (got it as 9) over the hypotenuse (don't have it).  We solve for the hypotenuse using Pythagorean's Theorem:

$c^2=2^2+9^2$ so

$c^2=85$ and

$c=\sqrt{85}$

Now we can find the sin of theta:

$sin\theta=\frac{9}{\sqrt{85} }$

We have to rationalize the denominator now.  Multiply the fraction by

$\frac{\sqrt{85} }{\sqrt{85} }$

Doing that gives us the final

$\frac{9\sqrt{85} }{85}$

third choice from the top