Question

Find the exact value of sin(arctan(2)).

Answer 1

what triangle corresponds to arctan(2) ?

Answer 2

it doesnt say but im assuming a right triangle

Answer 3

yes, but which right triangle?
if we have\[\tan^{-1}(2)=\theta\implies\tan\theta=\frac{\sin\theta}{\cos\theta}=2\]

Answer 4

so we are then left with sin(sin 2/cos 2)

Answer 5

no, we want the arctan of 2. not tan of 2

Answer 6

remember the definitions of sine and cos

Answer 7

so cos is on the top and sin on the bottom?

Answer 8

why do you think that?

Answer 9

do you know what arctan means?

Answer 10

arctan is the opposite of tan

Answer 11

in a sense... arctan(x) is the angle t at which tan(t)=x

Answer 12

I think you have confused it with the cotangent

Answer 13

tan= opposite/adjacent so that 2/1

Answer 14

yes

Answer 15

then we have to find the hypoteneus so we can get the sin

Answer 16

exactly :)

Answer 17

thats 2/sqrt5

Answer 18

yep :)
nice job

Answer 19

i see it makes since now. thank you!!

Answer 20

welcome, happy to help