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Vlad1618 [11]
3 years ago
13

There is a clown's face on the top of a spinner. The tip of his hat rotates to (−2, 5) during one spin. What is the cosine value

of this function?
−2


5


5 square root of 29 over 29


negative 2 square root of 29 over 29
Mathematics
1 answer:
Ivenika [448]3 years ago
6 0

Answer:

The last choice is your answer

Step-by-step explanation:

Plot your point in an x/y coordinate plane.  We are in QII where x is negative and y is positive.  From that point, if you drop an altitude to the negative x axis, you have a right triangle with a base measure of -2, a height of 5 and a hypotenuse that is unknown as of right now.  We will find it using Pythagorean's Theorem.  5^2+(-2)^2=c^2

The length of the hypotenuse is √29.  That means that the cosine of that angle is the side adjacent over the hypotenuse.  Rationalizing the denominator gives us -\frac{2\sqrt{29} }{29}

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The vertex is when x=-b/2a, which is also the line of symmetry. 
in this case, b=6, a=3, so x=-6/6=-1
when x=-1. y=3-6-1=-4

another way to do it is to write the equation into vertex form by making a square:
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