Question

how would I solve sin (2arctan 12/5) ?

Answer 1

do I have to use a double angle identity ?? if so how do I do that

Answer 2

first use your calculator to find arctan 12/5

Answer 3

im in a situation where I cant use a calculator actually but I do have all the values for y x and r

Answer 4

x is 5 y is 12 and r is 13

Answer 5

yes thats the 13-12-5 right angled triangle

Answer 6

mhm so sin is 12/13 but im unsure where to go next

Answer 7

sin 2x = 2sinx cosx

Answer 8

but wouldn't I use tan 2x + 2tanx/ 1-tan squared x ?

Answer 9

if sin is 12/13 whats the cos?

Answer 10

no

Answer 11

5/13

Answer 12

so I wouldn't use the double angle id for tan ? id use it for sin?

Answer 13

\(\bf sin\left[2tan^{-1}\left(\cfrac{12}{5}\right)\right]\implies sin(2\theta)\implies 2sin(\theta)cos(\theta)\\ \quad \\ \quad \\
a= 5\qquad b=12\qquad c=13\qquad thus\\ \quad \\
cos(\theta)=\cfrac{5}{13}\qquad sin(\theta)=\cfrac{12}{13}\qquad
2sin(\theta)cos(\theta)=2\left(\cfrac{12}{13}\right)\left(\cfrac{5}{13}\right)\)

Answer 14

omg. thank u so much

Answer 15

ok so plug into the formula for sin 2x as jdoe0001 has done

Answer 16

definitely keepin this on hand thanks everyone !!!

Answer 17

yw

Answer 18

arctan 12/5 means 'the angle whose tangent is 12/5'

Answer 19

yes, in this case \(\bf \theta\)

Answer 20

whatever angle that happen to be