# Angle Measurement

##
Angles are measured in degrees or radians. A complete circle has 360° or 2π radians. Therefore 360° = 2π radians.

Divide both sides by two and you have
180^{0} = π radians.

Therefore if we divide both sides by 180 we will find what 1° equals in radians.

180^{0}∕ 180 = π radians ∕ 180 → 1^{0} = π radians ∕ 180 →
1^{0} ≈ 0.01745329 radians.

( The above problem isn't any more difficult than 3t = 12

t would represent the degree symbol ^{0} 3t/3 = 12/3 → 1t = 12/3 → 1t = 4 )

Hence to change 15° to radians multiply both sides by 15 × 1^{0} = 15 × π radians ∕ 180 → π radians ∕ 12

π radians divided by 12 and we get 15^{0} ≈ .2617883878 radians. If we used (1^{0} ≈ 0.01745329 radians) × 15 ≈ .26179935.

We get a slightly different answer.

Due to rounding off the numbers involved in the calculations both answers are approximations.

However π radians ∕ 180 multiplied by 15 is a more accurate answer. Hence we used the latter instead of 0.01745329

What does 16^{0} =
answer

Our next consideration is that each degree equals 60 minutes and each minute equals 60 seconds.

So you can have a degree measurement of 13^{0}15' 11"

How do you change 13^{0}15' 11" to radian measure?
answer

Using the information that 180^{0} = π radians can you explain how to change

from radians to degrees? Hint 5 radians ≈ 286.478898^{o}
answer

What are: acute angles, obtuse angles, complementary angles, supplementary angles, straight angles

and right angles?
answer

return

return to PCTC