Question

Solve the equation, where 0° ≤ x < 360°. Round approximate solutions to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
3 sin x − 2 cos x = 1
..please solve.help me

Answer 1

hmm this is gonna require some attention
first i would want you to think of asin(x+b)=asinxsinb+acosxcosb

Answer 2

I want to achieve 3sinx-2cosx okay

Answer 3

if i set my first expression equal to that i would get
asinb=3 and acosb=-2

Answer 4

i need here find a first

Answer 5

now we need to recall the equation of a circle x^2+y^2=r^2
my r here is a
x=-2 and y=3
so \(r=\sqrt{(-2)^2+3^2}=\sqrt{13}\)

Answer 6

i mean \(a=\sqrt{13}\) now we need the angle b

Answer 7

so any idea how to get b?

Answer 8

@blowfish

Answer 9

i need tanb here i have tanb=sinb/cosb=-3/2
you can use arctan(-3/2)=? to get the angle and then go back to the original equal
that i wrote asin(x+b)=1 substitute a and b by the values you found and then solve

Answer 10

I think you got a pretty good idea here

Answer 11

I haven't got the right answer

Answer 12

what did you do?

Answer 13

Did you follow what i did

Answer 14

I squared both sides and substitute it in the quadratic formula

Answer 15

hmm squared both sides
i don't think that would work

Answer 16

show me what you did

Answer 17

what am I going to do, all I input in my quiz online were wrong.. will you solve it for me..what are the angles

Answer 18

(3sinx)^2=(2cosx+1)

Answer 19

(2cosx+1)^2

Answer 20

hmmm so what did you get after that

Answer 21

-2+or-2square root of 11 over 5

Answer 22

hmmm i don't think that gonna work pal?
you will be circulating for ever around to find something hehe

Answer 23

so can you find the angles?

Answer 24

i give you the method to get them

Answer 25

read my comments carefully
do what i suggested

Answer 26

I don't know how to manipulate it.. sorry

Answer 27

can someone help me pls.I tried it but can't find answers

Answer 28

Did you read what idid above from a to z
i give you everything you need to get this

Answer 29

Reread it again with attention

Answer 30

YEah I read it but really can't find the answer everytime I input my answer online

Answer 31

well, anyways, thank you so much for your effort but my assignment had closed already...

Answer 32

i don't think you read it
i said find b in asin(x+b)=1
tanb=-3/2 ====> artan(-3/2)=? use the calc to find b

Answer 33

a=root(13) i showed how we got it

Answer 34

hehe there was a time limit i see
Quiz then! My goal is to assist you not giving you direct answers
but at any rate me too i need a calculator to find b because it is a decimal angle
you can't do this in mind hehe