Question

without using a calculator, find the exact value of arccos(cos(17pi/5)). Justify your answer. Thanks

Answer 1

The arcos of a cos x is just "x". You are basically asking: give me the angle "x" whose cosine is the cosine of "x". It's just "x".

Answer 2

So, in this case, you want the angle whose cosine is the cosine of angle 17pi/5. That angle is 17pi/5.

Answer 3

All good now, @joselin12 ?

Answer 4

arccos() or \(cos^{-1}\)
means "what is the angle WHOSE cosine is THIS value?"

so

cos(x) is say "SOME NUMBER"

arccos(SOME NUMBER) means

"what is the angle WHOSE cosine is SOME NUMBER?"

well, it'd be "x"

Answer 5

not really

Answer 6

Work from the inside out. Concentrate on cos(17pi/5) first. That is going to give you a decimal number, a real, negative number between 0 and -1. You don't really care what it is at this point, but we can conceive of it as "y". Now you want the

arcos(y)

That's some angle where you already have a cos value. But you got that from doing the inside. So it's that angle (or, actually the equivalent in the range 0 to pi) that you started with.

Answer 7

oh i get it now, makes sense I was over thinking this. Thank you !!

Answer 8

uw!

Answer 9

you see, if the cos(17pi/5) = 1234567

so, arccos(1234567) is

what is the angle WHOSE cosine is 1234567? well, check above

Answer 10

One more thing, since the arcos function is defined for 0 to pi, you would subtract out 2pi from that 17pi/5 for an intermediate answer of:

7pi/5

but that's still not within 0 to pi, so using equivalent trig, you want:

3pi/5