Question

I can’t figure this out

Answer 1

Explanation:

To take a radian measure that is over 2π (360°), to an equivalent measure that is less than 2π, subtract intervals of 2π until the value is where you want it.

(23π)/4 - 2π = (23π)/4 - (8π)/4 = 15π/4

This is still more than 2π, so subtract another 2π...

(15π)/4 - 2π = (15π)/4 - (8π/4) = (7π)/4

This is less than 2π, so stop here...

following similar steps on the other 3 given radian measures give you...

(18π)/5 = (8π)/5

(22π)/9 = (4π)/9

(19π)/3 = π/3

To convert from degrees to radians, multiply the degree measure by π/180°

We have

60°(π/180°) = (60°π)/180° = π/3

288°(π/180°) = (288°π)/180° = (8π)/5

315°(π/180°) = (315°π)/180° = (7π)/4

80°(π/180°) = (80°π)/180° = (4π)/9

Answer 2

`\large{60^o\to(19\pi)/(3)\\\\288^o\to(18\pi)/(5)\\\\315^o\to(23\pi)/(4)\\\\80^o\to(22\pi)/(9)}`

Explanation:

`\text{The formula of conversion of degrees to radians:}\ (\theta \pi)/(180)\\\\360^o=2\pi\\\\60^o=(60\pi)/(180)=(\pi)/(3)\qquad(19\pi)/(3)=6\pi+(\pi)/(3)=(\pi)/(3)\\\\288^o=(288\pi)/(180)=(8\pi)/(5)\qquad(18\pi)/(5)=2\pi+(8\pi)/(5)=(8\pi)/(5)\\\\315^o=(315\pi)/(180)=(7\pi)/(4)\qquad(23\pi)/(4)=4\pi+(7\pi)/(4)=(7\pi)/(4)\\\\80^o=(80\pi)/(180)=(4\pi)/(9)\qquad(22\pi)/(9)=2\pi+(4\pi)/(9)=(4\pi)/(9)`