Question

i think the problem was sin(2x+3)=cos(30-x)
and we want to find the minimal value of x using the factor theorem
does this look right joe?

Answer 1

i found a solution but i don't how to use the factor theorem like that one guy asked for

Answer 2

yeah thats right, is there something more to this problem? i thought we solved it?

Answer 3

he wanted minimal value for x

Answer 4

and i have no clue how to use factor theorem to solve this

Answer 5

oh oh. i think by factor theorem he meant sum/difference formulas, it would be a long drawn out process >.<

Answer 6

is that what you were attempting?

Answer 7

yes, and i got tired lol >.<

Answer 8

lol
so i got x=pi/2-75

Answer 9

your solution was swift and fast, like a ninja.

Answer 10

but i don't know how i'm suppose to show its minimal value

Answer 11

there are other solutions

Answer 12

i guess i could do it my way and see what i get >.< give me an hour lol

Answer 13

Is the angles in degrees here

Answer 14

its in radians

Answer 15

inside the sin was 2x+45 tw

Answer 16

im sry, 2x-45

Answer 17

i remember negative root 2 over 2's popping up

Answer 18

roshan this is what i did earlier
\[\sin(2x+45)=\sin(\frac{\pi}{2}-(30-x))\]
\[2x+45=\frac{\pi}{2}-(30-x)\]

Answer 19

thanks joe

Answer 20

\[2x-x=\frac{\pi}{2}-30-45\]
\[x=\frac{\pi}{2}-75\]

Answer 21

trig functions are funky how do you know you have all the solutions

Answer 22

and i know i don't

Answer 23

this is too long, i dont wanna do it >.<

Answer 24

ok don't do it lol

Answer 25

your solution looks funny o.O are those numbers in degrees?

Answer 26

no

Answer 27

lol thats what rosahan asked lol

Answer 28

we also have the solution
\[x=-\frac{3\pi}{2}-75\]

Answer 29

75 almost like 12(2pi)....its like your flying around the unit circle redundantly o.O

Answer 30

if that is indeed radians.

Answer 31

i also checked it out wolfram to see if the solution worked and it did i think we can come up with something not so ugly

Answer 32

maybe not i'm not sure

Answer 33

\[x=\frac{5\pi}{2}-75 \] is another solution

i want to generalize my answer

Answer 34

oh i see how to :)

Answer 35

whats the pattern?

Answer 36

\[x=(-1)^{n}(2n+1)\frac{\pi}{2}-75, n=0,1,2,3,4,5,6...\]

Answer 37

now since this goes on and on there is no way to tell what is the smallest solution

Answer 38

Somehow my teacher told us to change the whole thing to sin theta and move it to one side.