Question

Find the solutions

Answer 1

the answer is 1.16+kpi but i have no idea where the 1.16 came from

Answer 2

Well just divide both sides by cosx
\[3\sin(x)=7\cos(x) \\ \\ \tan(x)=\frac{7}{3}\]

Answer 3

@.Sam. yeah thats what i got, but then the equation is 1.16+kpi and I dont know how that happend

Answer 4

That is in radian mode, can you use a calculator?

Answer 5

yes...i put it in the calculator and i did not get that answer..so turn it into radian mode?

Answer 6

okay i got it!

Answer 7

If its in degrees, is 66.8

Answer 8

Alright

Answer 9

and since tangent has a period of pi, every pi addition to its produces the same value

Answer 10

@amistre64 but sometimes for sin and cos there is more than one solution...how do you know when to stop

Answer 11

if it asks for ALL results, you never stop; that is what the addon of multiples of pi or 2pi represent

sin and cos are periodic (repeat themselves) every 2pi
tan is periodic (repeats itself) every pi

Answer 12

@amistre64 how about for this example find the solution for sin2x-cosx=0
this has i believe 4 solutions

Answer 13

sin 2x = 2 sinx cosx

factor our the cosx

cosx(2sinx - 1) = 0 when cosx=0, or sinx = 1/2

so yes, there are 4 values

Answer 14

each value has a period of 2pi attached to it as well