MATH SOLVE

2 months ago

Q:
# The measurement of a central angle is 75. Find the measurement of in radians

Accepted Solution

A:

Circumference = 360 degrees

Circumference = 2π radians (comes from 2*pi*radius)

Therefore

360 deg. = 2*π radians

180 deg. = π radians

1 deg. = (π/180) radians

75 deg. = 75(π/180) radians

75 deg. = 75π / 180 radians

don't bother to try and simplify π (it is an irrational number)

however you can simplify 75/180

both are divisible by 5

75π/180 = 15π/36

both are divisible by 3

75 deg. = 5π/12 radians

We normally don't bother to go further, unless you actually need it as a decimal fraction (in which case, you will have an approximation)

75 deg. ≈ 1.308997 radians

Circumference = 2π radians (comes from 2*pi*radius)

Therefore

360 deg. = 2*π radians

180 deg. = π radians

1 deg. = (π/180) radians

75 deg. = 75(π/180) radians

75 deg. = 75π / 180 radians

don't bother to try and simplify π (it is an irrational number)

however you can simplify 75/180

both are divisible by 5

75π/180 = 15π/36

both are divisible by 3

75 deg. = 5π/12 radians

We normally don't bother to go further, unless you actually need it as a decimal fraction (in which case, you will have an approximation)

75 deg. ≈ 1.308997 radians