Question

if sin theta=1/3, theta in quadrant II, find exact value of: b)sin(theta+pi/6)

Answer 1

don't put 1/3 for a do I?

Answer 2

sorry i dont get, i know about the formula, but not how to use it, theta?, what?+

Answer 3

you can put in 1/3 for sinA

Answer 4

B is pi/6

Answer 5

all you need is to find cosA ... and you have everything you need to use the formula

Answer 6

oh

Answer 7

how

Answer 8

and is pi/6 rad

Answer 9

how wud i find exact value of 1/3

Answer 10

so confused

Answer 11

\[\large \sin \left( \theta+\frac \pi6 \right)=\sin(\theta)\cos \left( \frac \pi6 \right)+\cos(\theta)\sin\left( \frac \pi6 \right)\] using the formula we get this .. ^^^

Answer 12

Yes that :P

Answer 13

yes pi/6 is in radians

Answer 14

how do we use 1/3 for the formula, where is hat coming in

Answer 15

well, if \(\ \sin(\theta) = \frac{1}{3}\), then \(\ \theta = \sin^{-1}(\frac{1}{3})\)

Answer 16

sin(θ) = 1/3 ... so , in the formula we can replace sin(θ) with 1/3.

Answer 17

Hint: you don't need to find theta

Answer 18

I can't see your post because there is inumerous amount of blackened question marks x_x

Answer 19

yeah , sorry ... it appears properly if you refresh.

Answer 20

buts lets

sin a = sin1/3

how wud i find exact value for thattt
?

Answer 21

pi/6 i wud understand

Answer 22

but the question does not say sin a = sin 1/3 ...???

Answer 23

no


theta = 1/3

Answer 24

so how do i find a??

Answer 25

sin theta = 1/3

there is no need to find theta.... we only need to find sin(theta + 6)

Answer 26

Ohh! yeah pax is right , haha. they're telling you that instead of finding the theta value for sin( theta), to replace sin(theta) with 1/3.

When you use the formula Pax and Akash posted, you will find the exact value you are looking for :)

Answer 27

ehh

Answer 28

\[\sin(\theta)=1/3\ ...\{\because given\}\]\[\sin\left( \frac \pi6\right)=\frac12\]\[\cos\left( \frac \pi6\right)=\frac{\sqrt3}2\] plug these numbers in

\[\large \sin \left( \theta+\frac \pi6 \right)=\sin(\theta)\cos \left( \frac \pi6 \right)+\cos(\theta)\sin\left( \frac \pi6 \right)\]\[\large \implies \sin \left( \theta+\frac \pi6 \right)=\frac13 \cdot {\sqrt3 \over 2}+\color{blue}{\cos(\theta)}\cdot \frac12\]

Answer 29

so we have all the numbers in the formula except \(\color{blue}{\cos(\theta)}\)
... which we can find using pythagorean theorem.

Answer 30

got it

Answer 31

vos wud be -2sqrt2 over 3

Answer 32

plug in

Answer 33

and u get sqrt 3 -2sqrt2 over6

Answer 34

i overthink

Answer 35

:p

Answer 36

wait wait.. how would we use the pythagorean theorem to find cos?

Answer 37

sin=o/h