Math  /  Trigonometry

QuestionQuestion 10 (1 point) The radian measure of an angle is defined as the length of the arc that subtends the angle divided by the radius of the circle. True False

Studdy Solution

STEP 1

What is this asking? Is the radian measure of an angle equal to the arc length divided by the radius? Watch out! Don't confuse radians with degrees!
Radians are all about arc length and radius.

STEP 2

1. Recall the definition of a radian.
2. Compare the definition with the statement.

STEP 3

Let's think about what a radian *actually* is!
A radian is a way to measure angles, just like degrees, but it's a bit more... mathematical!
Imagine a circle, any circle!
Now, imagine an arc along the edge of that circle.
The length of that arc, let's call it ss, plays a big role in defining a radian.

STEP 4

Now, think about the radius of that circle, let's call it rr.
The radius is the distance from the center of the circle to any point on its edge.
It's like the circle's special measuring stick!

STEP 5

A radian is defined as the angle formed when the arc length, ss, is *exactly equal* to the radius, rr.
In other words, when s=rs = r, the angle formed is **one radian**.

STEP 6

More generally, the measure of an angle in radians, let's call it θ\theta, is the ratio of the arc length, ss, to the radius, rr.
We can write this as: θ=sr \theta = \frac{s}{r}

STEP 7

The problem states: "The radian measure of an angle is defined as the length of the arc that subtends the angle divided by the radius of the circle."

STEP 8

This is *exactly* the same as our definition of a radian: θ=sr\theta = \frac{s}{r}, where θ\theta is the angle in radians, ss is the arc length, and rr is the radius.

STEP 9

The statement is **True**!

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