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(a) Find an angle between 0 and 2pi that is coterminal with 10pi/3.(b) Find an angle between 0° and 360° that is coterminal with -300°.Give exact values for your answers.(a) __ radians(b) __ °

Sagot :

To find a coterminal angle between 0 and 2pi, you can subtract 2pi from the given angle, like this

[tex]\frac{10\pi}{3}-2\pi\text{ }[/tex]

To do the subtraction, you can convert 2pi into a fraction, like this

[tex]\frac{2\pi\cdot3}{3}=\frac{6\pi}{3}[/tex]

So, you have

[tex]\frac{10\pi}{3}-2\pi=\frac{10\pi}{3}-\frac{6\pi}{3}=\frac{4\pi}{3}[/tex]

Therefore, 4pi/3 is the angle between 0 and 2pi that y is coterminal with 10pi/3.

For point (b), you can add 360° at the angle given, like this

[tex]360+(-300)=360-300=60[/tex]

Therefore, an angle between 0° and 360° that is coterminal with -300° is 60°.

View image QiL532810
View image QiL532810
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