Question

find cos(sin-1(3/5))

Answer 1

Draw a right angled triangle.

Answer 2

done

Answer 3

can't you just plug it in your calculator? find the inside function and then put that value into the cos equation?

Answer 4

no calculator allowed

Answer 5

Yes, you can put it in you calculator... and learn nothing.

Answer 6

OK so a triangle has an angle (x) - if sin of this angle is 3/5, then one side of the triangle is 3, and the other 5 (by definition). Use pythagoras to work out the other side, and then cos (by definition).

Answer 7

x = sin^-1(3/5), by the way

Answer 8

sin(a) = 3/5

sin^2 + cos^2 = 1

(3/5)^2 + cos^2 = 1

cos^2 = 1 - 9/25

cos^2 = 16/25

cos(a) = 4/5

Answer 9

cos-1(cos(a)) = 4/5

Answer 10

cos^-1(cos(a)) = a, actually ;)

Answer 11

hmm..... thats right. lol

Answer 12

there aint no simple angles from trig to give you a cosine of 4/5; or a sin of 3/5 :)

Answer 13

the answer is 4/5 right?

Answer 14

Yes (but my method was better :p)

Answer 15

what would cos(sin(3/5)) be?

Answer 16

That would be .. a lot harder (if neither are ^-1)

Answer 17

sorry cos-1(sin(3/5))

Answer 18

woops

Answer 19

\[\cos^{-1}\left[\sin\left(\frac{3}{5}\right)\right] = x \iff \sin\left(\frac{3}{5}\right) = \cos(x)\]

Answer 20

Are you working in radians or degrees?

Answer 21

radians i assume. the problem calls for the exact value

Answer 22

By definition: \[\sin(\alpha) = \cos\left(\frac{\pi}{2}-\alpha\right) \text{ and } \cos(\alpha) = \sin\left(\frac{\pi}{2}-\alpha\right) \]

Answer 23

So if sin(3/5) = cos(x), then x = ....

Answer 24

3/5 ?

Answer 25

im sorry those formulas are in my book and i can't understand them.

Answer 26

They aren't in your book, do you mean?

Answer 27

are. i have example problems i just wanted it broken down.

Answer 28

i have to go. thanks for the bit of help though! sorry i couldn't do more with it

Answer 29

Oh, OK. Well, they work because cos is just a translation of sin, by pi/2. The answer is x = pi/2 - 3/5, from the formulae