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

1 answer:

5 0

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

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