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,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]Hypotenuse^2=(5)^2+(2)^2[/tex]
[tex]Hypotenuse^2=25+4[/tex]
Taking square root both the sides.
[tex]Hypotenuse=\sqrt{29}[/tex]
In a right angled triangle,
[tex]\cos \theta=\frac{Base}{Hypotenuse}[/tex]
Substitute Base=2 and [tex]Hypotenuse=\sqrt{29}[/tex] in the above equation.
[tex]\cos \theta=\frac{2}{\sqrt{29}}[/tex]
Rationalize the denominator.
[tex]\cos \theta=\frac{2}{\sqrt{29}}\times \frac{\sqrt{29}}{\sqrt{29}}[/tex]
[tex]\cos \theta=\frac{2\sqrt{29}}{29}[/tex]
In 2nd quadrant cosine values are negative. So,
[tex]\cos \theta=-\frac{2\sqrt{29}}{29}[/tex]
Therefore the correct option is D.
