A car is travelling to the right with a speed of 42\,\dfrac{\text m}{\text s}42 s m 42, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction when the driver slams on the brakes. The car skids for 4.0\,\text s4.0s4, point, 0, start text, s, end text with constant acceleration before it comes to a stop. What is the displacement of the car as it skids to a stop?

Answers:

sin(x) = 3/5

cos(y) = 3/5

They are both equal to the same value

Explanation:

Use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2

8^2+6^2 = c^2

100 = c^2

c^2 = 100

c = sqrt(100)

c = 10

The hypotenuse is 10 units long.

Now compute the sine of angle x.

sin(angle) = oppposite/hypotenuse

sin(x) = 6/10

sin(x) = 3/5

Also, find the cosine of angle y

cos(angle) = adjacent/hypotenuse

cos(y) = 6/10

cos(y) = 3/5

It turns out that sin(x) = cos(y) if and only if x+y = 90.