Question

How do you find the arctan 4/3 ? (Without a calculator)

Answer 1

You could draw a right triangle with sides of lengths 4 and 3, then measure the angle made by the hypotenuse

Answer 2

How do I do that WITHOUT a calculator?

Answer 3

With a ruler and a protractor

Answer 4

No, the problem is to find the exact value of the expression: sing(arctan 4/3)

Answer 5

sin*

Answer 6

Oh, well that's a totally different question

Answer 7

If you have a right triangle with sides 4 and 3 do you see why the angle made by the hypotenuse is the arctan of 4/3?

Answer 8

yes I get that, but I feel asleep during notes so I have no idea how to do this part...

Answer 9

what's the definition of sin(x) if you have a right triangle?

Answer 10

Opp/ hyp**

Answer 11

that's tan(x) -- opposite over adjacent. sin(x) is opposite over hypotenuse.

Answer 12

So you want to compute opposite/hypotenuse of an angle whose arctan is 4/3. if you draw a triangle with sides 3 and 4, how long is the hypotenuse?

Answer 13

5

Answer 14

right, so you've got a 3-4-5 triangle. One of those angles will be the arctan of 4/3 -- the angle for which 4 is the opposite and 3 is the adjacent. Now sin of that angle is opposite over hypotenuse. which is...?