If the arc length shown in blue is 15.5 inches, then theta to the nearest hundredth of a radian is?

1 answer:

3 0

If you need to refer to the figure you can open the pdf file that I attached.

If you do not know the relationship between arc lengths and angles in radians, you can derive it from the circumference of a circle. This is how:

[2π rad / 2π R] = [x / arc] , where R is the radius of the circle, arc is the length of the arc, and x is the angle in radians.

You can solve for the angle x.

x = arc / R

In the figure arc = 15.5 inches, R = 12 inches, and theta is the unknown angle. Then:

theta = arc / R = 15.5 / 12 = 1.29167 radians.

Which rounded to the nearest hundreth is 1.29

Answer: 1.29 radians

Download pdf

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Since $m$ represents the slope, substitute $-\frac{1}{3}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, choose any one of the given points (it doesn't matter which one) and substitute the x and y values of it into the formula. (I chose (1,-4), as seen below). This gives the equation of the line in point-slope form.

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