Question

can someone please help me! please! i have a test in an hour!

Answer 1

for sin3x = 1/2 why is the answer pi/18 and 5pi/18 ?

Answer 2

That is not a math question. This might be better suited for chat.

Answer 3

first thing. dont panic.
we ll help you but this last minute thing wont help you now.
what ll help you is staying calm to focus your mind and use you intelligence.

have confidence mate, it wont be so bad (never is)!!! :)))

Answer 4

start with
\[\sin(3x)=\frac{1}{2}\] now forget about the 3x for a moment, just figure out what angle (number) as sine of 1/2
if you are working in degrees, on such angle is 30
in radians it is
\[\frac{\pi}{6}\]

Answer 5

so you have
\[3x=\frac{\pi}{6}\] and so
\[x=\frac{\pi}{18}\] is one possible answer

Answer 6

where do you get the pi over 6?

Answer 7

ok so now for some of these there are more than one solution (because they can be in different quadrants) how do you know which quadrant?

Answer 8

it is also true that

\[\sin(\frac{5\pi}{6})=\frac{1}{2}\] and so
\[3x=\frac{5\pi}{6}\] therefore
\[x=\frac{5\pi}{18}\]

Answer 9

are you asking how i know that
\[\sin(\frac{\pi}{6})=\frac{1}{2}\]?

Answer 10

mmm i don't think so I'm asking like

Answer 11

if i have sin 3x = 1/2 why are there 2 answers?

Answer 12

look at the last page of the attached cheat sheet. sine is the second coordinate so find the places on the unit circle where the second coordinate is 1/2

Answer 13

there are not two answers, there are an infinite number of answers because sine is periodic. so there are an infinite number of numbers whose sine is 1/2

Answer 14

i just gave an example of two of them

Answer 15

hmmm so if i had 4 sinx + 3 = 1

Answer 16

i would first do 4 sinx = -2 so sinx = -1/2

Answer 17

start with
\[\sin(x)=-\frac{1}{2}\]

Answer 18

since sin is y/R then would it be in quadrant III and IV because thats where y value is negative?

Answer 19

then look on the unit circle for the angles where the second coordinate is -1/2

Answer 20

oh i see! so hmmmmm what if i had tan = -3 /4

Answer 21

you will see two possibilities,
\[\frac{7\pi}{6}\]or
\[\frac{11\pi}{6}\]

Answer 22

how do i do that because i don't know if the 3 (y) or the 4 (x) is negative

Answer 23

if you have
\[\tan(x)=-\frac{3}{4}\] you will need a calculator

Answer 24

how do i know if the y or x value is negative?

Answer 25

need to use
\[x=\tan^{-1}(-\frac{3}{4})\]

Answer 26

you don't

Answer 27

you could either be in quadrant II or IV

Answer 28

hmmmm.. why those quadrants?

Answer 29

because in quad II sine is positive but cosine is negative, so tangent will be negative
in quad IV sine is negative and cosine is positive, so tangent will be negative

Answer 30

ohh! that makes a lot of sense. do you think you could give me a few problems to try? like just 2 or 3?

Answer 31

\[2\sin(2x)=\sqrt{3}\]

Answer 32

\[\sqrt{3}\tan(x)=1\]

Answer 33

lets see x = sqrt 3 y = 1 and r = 2

Answer 34

now this must be in quadrant 1 or 3 since x and y are positive (they could both pbe positive or both be negative)

Answer 35

30 degress or 210 degres

Answer 36

that is rigth for the first one!

Answer 37

:DDDDD

Answer 38

how would you do 3 - sinx = 2sin x?