# Thread: Need help with a problem: arcsin(x-1/2)-arccos(x-1/2)=3pi/2

1. ## Need help with a problem: arcsin(x-1/2)-arccos(x-1/2)=3pi/2

arcsin(x-1/2)-arccos(x-1/2)=3pi/2

not really familiar with formatting on this site, but here's the problem. is there a formula i could perhaps use??

2. Formula:

1) Have I EVER seen anything like this?
2) Does it look AT ALL like it could be solved?
3) How might I proceed if it were simpler-looking?
4) Has trigonometry shown me anything at all about how to deal with the difference of two angles?
5) If I introduced a sine or a cosine, which might be more convenient?

3. Originally Posted by starkiller
arcsin(x-1/2)-arccos(x-1/2)=3pi/2

not really familiar with formatting on this site, but here's the problem. is there a formula i could perhaps use??
Tkhunny's suggestions are good. I'll add one thing: when I face a problem involving inverse trig functions, I commonly define new variables like this:

A = arcsin(x-1/2) so that sin(A) = x - 1/2
B = arccos(x-1/2) so that cos(B) = x - 1/2

Then the equation becomes A - B = 3pi/2. Now, you might take the sine or cosine of both sides. I haven't fully pursued the solution, but I think you'll find that there's no actual solution when you check it. (I base that on consideration of the ranges of the two functions.) Are you sure you copied it correctly?

By the way, you've formatted your equation just right. There's no need for the fancy stuff if you don't plan to become an expert.

4. no i've copied it just fine and the answer is -1/2. i could guess that based on the answer options but i can't figure out an actual way to solve it

Did you calculate:

A - B = 3π/2

sin (A - B) = sin(3π/2)

continue......

6. Originally Posted by starkiller
no i've copied it just fine and the answer is -1/2. i could guess that based on the answer options but i can't figure out an actual way to solve it
Yes, that answer is correct. I had a sign wrong when I checked my answer in my head. Have to learn not to do that...

By the way, when you state a problem, you should always include the answer choices if it is multiple-choice; sometimes that has a major effect on the nature of a problem.

7. thanks for pointing me in the right direction, appreciate that. i'm sure the solution is apparent, but i still can't, for the life of me, figure it out. what does sin(a-b)=-1 give us?

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