Question

Suppose that sin(theta)=3/5 and theta is in the second quadrant. Find sin(2(theta)), cos(2(theta)), and tan(2(theta)) exactly.

Answer 1

use arcsin(3/5) to find theta

Answer 2

i don't even know what arcsin(3/5)
my instructor just does the problems while talking to himself, and i don't get it how he does them. That's why i'm always stuck for 10 hours only on my math homework.

Answer 3

You have to use a calculator.

Answer 4

Unless rouault knows of a unit circle measure that we can use. I'm going to have to wimp out on this one. Too tired. Sorry :/

Answer 5

so
sin2theta=2sin(theta)cos(theta)

Answer 6

i assume this is Double-angle identities right?

Answer 7

sin(theta)=3/5
theta=arcsin(3/5)

sin(2arcsin(3/5))
double angle identity
sin(2arcsin(3/5)) = 2sin(arcsin(3/5))(cos(arcsin(3/5))
and so on

Answer 8

arcsin? isn't that the same thing as
sin2x=2sin x cos x
cos 2x=cos^2 x -sin^2 x
=1-2 sin^2 x
=2 cos^2 x-1
tan2x=(2tanx)/(1- tan^2 x)

Answer 9

its inverse, instead of from angle to sides its from sides to angles

Answer 10

arcsin means to ask the calculator what the degree was for sin.
For example, (I'm making up numbers here),
sin50 = 13/12
but arcsin 13/12 = 50

Note that those numbers are not factual.

Answer 11

to solve this, instructor indicated to use Double-angle identities

Answer 12

this is what i got
\[\sin2\theta=\frac{-24}{5}\]
\[\cos2\theta=\frac{7}{25}\]
\[\tan2\theta=\frac{-24}{7}\]

Answer 13

to solve cos(arcsin(3/5)) find out what the triangle is for arcsin(3/5) looks like. It is a 3 4 5 righttriangle in standard position. Find the cos of that tringle and you have the answer, 4/5

Answer 14

sin(arcsin(theta)) will cancel since they are inverse of eachother

sin(arcsin(theta))= theta

Answer 15

the answer to the first one is 24/25

Answer 16

or rather, using theta is sort of confusing, sin(arcsin(3/5))= 3/5

Answer 17

Rouault thanks. I've got to move on. have a wonderful day.