Question

Can someone help walk me through this? Any help would be greatly appreciated! ..... (a) Find an angle between 0 and 2π that is coterminal with 7π/2 (b) Find an angle between 0° and 360° that is coterminal with -225° Give exact values for your answers. (a) ____ radians (b) ____ °

Answer 1

Answer:

a) 3π/2

b) 135°

Step-by-step explanation:

Coterminal angles are angles in standard position that end at the same place (their terminal sides).

Think of the angle 60° on the unit circle. If you wanted to find a coterminal angle to 60°, then you would just have to add 360° or some multiple of 360 (ie; 720°, 1080°, 1440°, etc. would all work too). Or you could go the opposite direction and subtract 360°(aka adding -360°) or some multiple of that. The only difference for radian measures is that you add or subtract a multiple of 2π. If you, again, think of the unit circle, then it'd be like rotating the angle around until you reach the same spot.

So for your problems, you're given two angles that are outside the domain of 0 to 360°(or 2π). Essentially you just need to add or subtract 360°(or 2π) until you're within the desired domain:

• 7π/2 is greater than 2π [2π = 4π/2], so subtract 2π from this
• -225° is less than 360°, so add 360° to this one

For these two you only need to do each one once to give you the coterminal angles above.