Question

hello i dont understand what they are asking in this question, "Find all of the solutions that satisfy sin 2x + 3cos, x = 0"? . its a calculus question btw

Answer 1

it's asking you to solve for x in the equation sin(2x) + 3cos(x) = 0

Answer 2

could u plz give me few first steps??

Answer 3

are you know the rule of sin2x

Answer 4

2sinxcosx??

Answer 5

yeah apply it
then what you get?

Answer 6

cosx(2sinx+3)??

Answer 7

right :)
then you have to divide all the two sides of the equation by cosx
the result is...?

Answer 8

sinx=-3/2?

Answer 9

good :)
then x=?

Answer 10

yea i dont understand the next step could u tell me ?

Answer 11

if you have the equation
sintheta=A
theta=sin^-1 A

Answer 12

\[x=\sin ^{-1}\frac{ -3 }{ 2 }\]

Answer 13

got it?

Answer 14

oh ok so do i put it in my calculator??

Answer 15

yeah

Answer 16

wait i get a math error?? beacuse of that negative sign

Answer 17

ok

Answer 18

so what should i do?

Answer 19

240 in dgree

Answer 20

\[2\sin(x)\cos(x)+3\cos(x)=\cos(x)(2\sin(x)+3)=0\]
find when both factor are equal to zero
2sin(x)+3 is never zero because sin(x) is never -3/2 because the range of sin(x) is from -1 to 1
so you only need to solve cos(x)=0

Answer 21

wait so after that i just look atthe unit circle?

Answer 22

so the answer is 1 ?

Answer 23

nope x isn'1
cos(1) is not 0

Answer 24

find for what angles cos is 0

Answer 25

when are the x-coordinates on your unit circle sheet 0? for what angles?

Answer 26

90?

Answer 27

that is one yep
are there any others?

Answer 28

270?

Answer 29

so it would be \[90^o+180^o \cdot n \text{ where n is an integer }\]

Answer 30

wait what so the soltion is not 90 and 270??

Answer 31

Those are some of the solutions
You were asked to find all so I helped you out a bit in doing so.
The solution I gave contains both of those solutions and many more.