Question

There is a clown’s face on the top of a spinner. The tip of his hat rotated to (-2, 5) during one spin. What is the cosine value of this function?
A) -2
B) 5
C) 5 sqrt 29/29
D) -2 sqrt 29/29

Answer 1

Answer:

The correct option is D.

Step-by-step explanation:

It is given that the clown’s face on the top of a spinner. The tip of his hat rotated to (-2, 5) during one spin.

In the point (-2,5), x-coordinate is negative and y-coordinate is positive, it means the point lies in 2nd quadrant. In 2nd quadrant cosine values are negative.

From the below figure it is clear that triangle ABO is a right angled triangle, with perpendicular 5 and base 2.

According to the Pythagoras theorem,

$Hypotenuse^2=Perpendicular^2+Base^2$

$Hypotenuse^2=(5)^2+(2)^2$

$Hypotenuse^2=25+4$

Taking square root both the sides.

$Hypotenuse=\sqrt{29}$

In a right angled triangle,

$\cos \theta=\frac{Base}{Hypotenuse}$

Substitute Base=2 and $Hypotenuse=\sqrt{29}$ in the above equation.

$\cos \theta=\frac{2}{\sqrt{29}}$

Rationalize the denominator.

$\cos \theta=\frac{2}{\sqrt{29}}\times \frac{\sqrt{29}}{\sqrt{29}}$

$\cos \theta=\frac{2\sqrt{29}}{29}$

In 2nd quadrant cosine values are negative. So,

$\cos \theta=-\frac{2\sqrt{29}}{29}$

Therefore the correct option is D.

Answer 2

A lot of the people out there are saying that the answer is negative 2 over sqrt 29. However, I am doing the test, and if you multiply the top and bottom by sqrt of 29, you get D, which is -2 sqrt29/29