Which of the following could be a coterminal angle for -5pi/4?
19pi/4
7pi/4
-17pi/4
-25pi/4
I've done my math twice, but I can't seem to get the right answer:( pls help?
coterminal means a complete circle (s) away
2π is a full circle ... 8π/4 in this case
-5π/4 ± n(8π/4) ... n is an integer value
This ends up giving me 3pi/4, which is what I've been getting... at this rate I'm pretty sure I'm going something wrong, I don't know what to do from here.
what if n=3 ?
Well, it seems like you're having a real "angle" of a problem here! Don't worry, I'm here to clown around and help you out!
To get coterminal angles, all we need to do is add or subtract 2π (or a full revolution) from the original angle.
Now, let's give it a go!
Starting with -5π/4, let's add 2π to it:
-5π/4 + 2π = 3π/4
Ah, so we have found a coterminal angle of 3π/4.
Now, let's check if any of the given options match our result:
19π/4 - No, that's not the one.
7π/4 - Nope, not it either.
-17π/4 - Oh, no, that's not our angle.
-25π/4 - Sorry, that's not the right one either.
So, it looks like the only coterminal angle for -5π/4 is 3π/4.
Keep up the good work, and remember, angle problems can be a little tricky, but with a sprinkle of humor, anything is possible!
To find the coterminal angles for -5π/4, you need to add or subtract integer multiples of 2π until you reach angles that are equivalent.
First, let's think about adding multiples of 2π. To do this, you can add 2π to the given angle -5π/4 until you get a positive angle.
-5π/4 + 2π = -5π/4 + 8π/4 = 3π/4
This means that -5π/4 and 3π/4 are coterminal angles because they both point in the same direction.
Now, let's think about subtracting multiples of 2π. To do this, you can subtract 2π from the given angle -5π/4 until you get a negative angle.
-5π/4 - 2π = -5π/4 - 8π/4 = -13π/4
This means that -5π/4 and -13π/4 are coterminal angles because they both point in the same direction.
Now, let's check which of the answer choices match these coterminal angles:
- 19π/4: This angle is not coterminal because it rotates in the opposite direction.
- 7π/4: This angle is not coterminal because it rotates in the opposite direction.
- -17π/4: This angle is coterminal because it points in the same direction as -5π/4.
- -25π/4: This angle is not coterminal because it rotates in the opposite direction.
Therefore, the coterminal angles for -5π/4 are -13π/4 and -17π/4.
I hope this helps! Let me know if you have any further questions.