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  180⁰ = π radians.

Therefore if we divide both sides by 180 we will find what 1° equals in radians.
180⁰∕ 180 = π radians ∕ 180 → 1⁰ = π radians ∕ 180 → 1⁰ ≈ 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 × 1⁰ = 15 × π radians ∕ 180 → π radians ∕ 12
π radians divided by 12 and we get 15⁰ ≈ .2617883878 radians. If we used (1⁰ ≈ 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 16⁰ =  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  13⁰15' 11"

How do you change 13⁰15' 11" to radian measure? answer

Using the information that  180⁰ = 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

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