Question

How would you solve this without a calculator?

cos (tan^-1(2/3))

Answer 1

start by drawing a right triangle with one angle theta, adjacent side 3 and opposite 2
i.e. tan(theta) = 2/3 got that?

Answer 2

Yes, then you do the pythagorean theorem to get the hypotenuse which is 13 right?

Answer 3

yes but its sqrt13. do you know what to do next?

Answer 4

Ok. No what do I do next

Answer 5

ok, theta = tan^-1(2/3) so cos(tan^-1(2/3) = cos(theta)

which you can work out from your triangle!

Answer 6

I don't really understand

Answer 7

Do you mean figure out tan^-1(2/3) first then whatever that answer is take the cos of?

Answer 8

if tan(theta) = 2/3 then theta = tan^-1(2/3) happy with that?

Answer 9

So regardless you have to already know what tan^-1(2/3) is? Like have the unit circle memorized with the tangents?

Answer 10

no you dont have to memorise anything because we are not going to work out what theta is.

do you follow what i did before?

Answer 11

great diagram and theta will be on the bottom left.

do you understand about theta = tan^-1(2/3)?

Answer 12

The only thing I get from that is that you have to know that value

Answer 13

Which I can figure out if I know the unit circle

Answer 14

What do you mean by that?

Answer 15

no, you are stuck on thinking that you need to know the angle theta and you dont

can you see that theta = tan^-1(2/3), because we have not finished yet

Answer 16

Ok yes, so theta is still undefined

Answer 17

yes and it will stay that way

now going back to the beginning cos(tan^-1(2/3)) = cos(theta) and we can work out cos(theta) from your triangle!

Answer 18

Ok.. so cos is adjacent over hypotenuse, and that would be 3/sqrt13? Is that what you mean?