Question

If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and π/2. what is cos(x-y)?

Answer 1

Well the sec(y) = 5/4 is just cos(4/5)

Answer 2

\[\sin (x) = \frac{1}{3} \rightarrow x = \sin^{-1} \left( \frac{1}{3} \right)\]\[\sec(y) = \frac{5}{4} \rightarrow y = \sec^{-1} \left( \frac{5}{4} \right)\]

Answer 3

so it's like.. \[\cos (\frac{ \sin^{-1} (1/3) }{ \cos^{-1} (4/5) })\]

Answer 4

what is the formula of cos(x-y) ?

Answer 5

what on earth?
\[\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)\] you need all 4 numbers, lets see how many you have

Answer 6

so thats...\[\frac{ 1 }{ 15 }(3 + 8\sqrt{2})\]

Answer 7

you've got \(\sin(x)\) because you are told it is \(\frac{1}{3}\)

Answer 8

Oops.. did i work too fast.

Answer 9

sec(y) = 1/cos(y) = 4/5, from here you can get what cos(y) is.

Answer 10

you've got \(\cos(y)\) as it is \(\frac{4}{5}\) so what is missing?

Answer 11

I think i got it.. ?

Answer 12

missing
\(\sin(y)\) and also \(\cos(x)\) which you find via pythagoras

Answer 13

well for the interval 0 -> pi/2.. i just need the positives right..

Answer 14

then i need the angle whose sine is 1/3 and the angle whose cosine is 4/5..

Answer 15

and then i subtracted them, my bad i out it as a fraction..

Answer 16

it should be \[\cos (\sin^{-1} (1/3) - \cos^{-1} (4/5)) = \frac{ 1 }{ 15 } (3 + 8\sqrt{2})\] ?

Answer 17

@satellite73