Math 3 Unit 6 Lesson 5

Front

What is the formula for arc length when θ is in radians?

Back

Arc length = r * θ, where r is the radius and θ is in radians.

Front

How do you convert radians to degrees?

Back

Multiply the radian measure by \( \frac{180}{\pi} \).

Front

What is the formula for the area of a sector?

Back

Area = \( \frac{1}{2} r^2 θ \), where r is the radius and θ is in radians.

Front

Convert \( \frac{4\pi}{3} \) radians to degrees.

Back

240 degrees.

Front

What is the value of 510 degrees in radians?

Back

\( \frac{17\pi}{6} \) radians.

Front

How do you find the area of a sector given the radius and angle?

Back

Use the formula: Area = \( \frac{1}{2} r^2 θ \).

Front

What is the relationship between degrees and radians?

Back

180 degrees = \( \pi \) radians.

Front

How do you round a number to the nearest tenth?

Back

Look at the hundredths place; if it's 5 or more, round up.

Front

What is the area of a sector with a radius of 10 cm and an angle of \( \frac{2\pi}{3} \) radians?

Back

Area = \( \frac{1}{2} (10^2) (\frac{2\pi}{3}) = \frac{100\pi}{3} \approx 104.7 \ cm^2 \).

Front

What is the formula to convert degrees to radians?

Back

Multiply the degree measure by \( \frac{\pi}{180} \).