Trig Equation: Solve for x?

Question

Solve for x

sinxtan3x=0 [-π,0]


The answer is supposed to be x = 0, -π, 3π/4, -3π/4 but I have no clue how to simplify the above equation. Please show steps.

sbjnyc, the solutions I included was from the back of my textbook .. maybe they're wrong?

Answer 1

You don't really need to simplify it.

Any number times 0 is 0 so if sinx=0 or if tan3x=0 the equation is satisfied.

if sinx=0 then x=0 or x=-π
if tan3x=0 then 3x=0 -> x=0 or 3x=-π -> x=-π/3

So the soilutions are x=0, -π/3, -π

I'm not sure how you got the solutions 3π/4, -3π/4 because the first one is not in the interval and the second one doesn't work.

Answer 2

sinx tan 3x = 0
sinx = 0 or tan3x = 0

sinx = 0 when x = 0 or -π
tan3x = 0 when x = 0 or -π so x = -π/3

So I don't know how you got the -3π/4 answer.

Answer 3

A * B = 0 tells us that either A = 0 or B = 0
So either sin(x) = 0 in which case x = integer multiples of pi
or tan(3x) = 0 in which case 3x = integer multiples of pi

etc etc for your case with interval [-π,0]

Answer 4

Break it up

if sin x = 0 then everything else is canceled
if tan 3x = 0 then again, everything else is canceled

So find where sin is 0 between - pi and 0
it is 0 and -pi from sin x which is the first two answers.
That is as far as I can get you

Just graph tan 3x and see where it crosses the x axis.

Answer 5

((a million +sinx)/ cosx) + (cosx/(a million+sinx))= 4 (a million +sinx)^2 + (cosx)^2 = 4(a million +sinx)(cosx) a million + 2 sinx + sin^2 x + cos^2 x = 4 cos x + 4 sin x cos x a million + sin x = 2cos x ( a million +sin x) (a million + sin x)(a million -- 2 cos x) = 0 giving sin x = -- a million OR x = n(pi) + (--a million)^n (-- pi/2) and cos x = a million/2 OR x = 2n(pi) +/-- (pi/3)

Answer 6

lets try:

sinxtanx=0

sinx(sinx/cosx) = 0

sin^2x / cosx = 0

cross multiply

sin^2x=0

square root both sides

sinx=0

x=0