Respuesta :
Answer:
[tex]\large{60^o\to\dfrac{19\pi}{3}\\\\288^o\to\dfrac{18\pi}{5}\\\\315^o\to\dfrac{23\pi}{4}\\\\80^o\to\dfrac{22\pi}{9}}[/tex]
Step-by-step explanation:
[tex]\text{The formula of conversion of degrees to radians:}\ \dfrac{\theta \pi}{180}\\\\360^o=2\pi\\\\60^o=\dfrac{60\pi}{180}=\dfrac{\pi}{3}\qquad\dfrac{19\pi}{3}=6\pi+\dfrac{\pi}{3}=\dfrac{\pi}{3}\\\\288^o=\dfrac{288\pi}{180}=\dfrac{8\pi}{5}\qquad\dfrac{18\pi}{5}=2\pi+\dfrac{8\pi}{5}=\dfrac{8\pi}{5}\\\\315^o=\dfrac{315\pi}{180}=\dfrac{7\pi}{4}\qquad\dfrac{23\pi}{4}=4\pi+\dfrac{7\pi}{4}=\dfrac{7\pi}{4}\\\\80^o=\dfrac{80\pi}{180}=\dfrac{4\pi}{9}\qquad\dfrac{22\pi}{9}=2\pi+\dfrac{4\pi}{9}=\dfrac{4\pi}{9}[/tex]
Answer:
Step-by-step 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