Question

If sin theta=3/5 and theta is in quadrant 2 determine in exact form sin theta+pi over 6

Answer 1

We have formula sin(a+b) = sin a *cos b + sin b *cos a
your a = theta
your b= pi/6
find cos theta, then plug all into it.

Answer 2

@Loser66 So I did all that and got the answer .9196 but I am off by a point when I check if it is right tho

Answer 3

show your work, please

Answer 4

Alright the end work I got 3sqrt3 over 10 + 2/5 but it doesn't come out correct -___-

Answer 5

cos (theta) = 4/5
hence sin (theta + pi/6) = sin (theta) cos (pi/6) + sin (pi/6) cos (theta)
= (3/5) (sqrt 3/2) + (1/2) (4/5) = 0.573

Answer 6

But I still keep getting .919... answer ohmygod this is so frustarting lol @Loser66

Answer 7

And when you go to check the answer it is suppose to be .90166

Answer 8

http://www.wolframalpha.com/input/?i=%283%2F5%29+%28sqrt%283%29%2F2%29+%2B+%281%2F2%29+%284%2F5%29+

Answer 9

that is what it says when I punch in what loser has above

Answer 10

and 0.9196 is also what I'm getting

Answer 11

i think you are right @shortyyshayy

Answer 12

and they have an error

Answer 13

@freckles Idk this is coming out weird cuz when checking it I am like a .1 off lol

Answer 14

just to be sure you are asked to evaluate
\[\sin(\theta+\frac{\pi}{6})\]

Answer 15

well the other thing is it says it wants the EXACT form
not an approximation

Answer 16

exact form would be
\[\frac{2}{5}+\frac{3 \sqrt{3}}{10}\]

Answer 17

not .9196

Answer 18

which is just an approximation

Answer 19

https://www.google.com/?gws_rd=ssl#q=online+calculator

Answer 20

omg I'm so dumb

Answer 21

I didn't see it said in quadrant 2

Answer 22

cos is negative there

Answer 23

\[\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2}\]

Answer 24

which actually gives us .1196
so that still doesn't give us the answer you want

Answer 25

yes!!! @freckles

Answer 26

where did you get -4/5 from tho??

Answer 27

it says theta is in quadrant 2

Answer 28

cos is negative there
and
sin is positive there

Answer 29

sin(theta)=3/5
cos(theta) can be 4/5 or -4/5 depending on where theta is

Answer 30

and since cos is negative then cos(theta)=-4/5

Answer 31

here is another way to look at it
we are given sin(theta)=3/5
\[\cos^2(\theta)+\sin^2(\theta)=1 \\ \cos^2(\theta)+(\frac{3}{5})^2=1 \\ \cos^2(\theta)+\frac{9}{25}=1 \\ \cos^2(\theta)=1-\frac{9}{25} \\ \cos^2(\theta)=\frac{25}{25}-\frac{9}{25} \\ \cos^2(\theta)=\frac{16}{25} \\ \cos(\theta)=\pm \sqrt{\frac{16}{25}} \\ \cos(\theta)=\pm \frac{4}{5}\]

Answer 32

now deciding whether to use 4/5 or -4/5 entirely depends on where theta is