how do i figure out this trig equation: tan(beta) = 2sin(beta)?

Question

equation:
tan(beta) = 2sin(beta)

so far i have...
sin(beta)/cos(beta) = 2sin(beta)/1

then cross multiply...
sin(beta)=2sin(beta)cos(beta)

now i'm stuck, what should i do next? thanks for the help.

Answer 1

It looks like you want to solve for β (beta). What you have so far is good, so lets just continue from there:

sin(β)=2sin(β)cos(β)

Divide both sides by sin(β)*:

1 = 2cos(β)

Divide both sides by 2:

cos(β) = ½

Take the arccos of both sides:

β = arccos(½) = π/3 = 60°

*sin(β) cannot be 0 (─► β cannot be zero) if you divide with it, because that would mean dividing by zero, which is an undefined operation.

Plug in β = 0 to see if it is a solution:

tan(0) = 2sin(0) ──► 0 = 0

So 0 IS a solution, and your solution set is:

β = {0, π/3}

Answer 2

Lets consider sin(beta) not equal to zero
(if sin(beta) equals zero then it is an undetermined equation 0=0)

tan(beta)=2sin(beta)
sin(beta)/cos(beta)=2sin(beta)
sin(beta)=2sin(beta).cos(beta)

divide both sides of the equation by sin(beta) and you get:

1=2cos(beta)
cos(beta)=1/2

if you want to find beta just look for angles that have cos = 1/2

cos(beta)

Answer 3

You went down the worng path by cross multiplying.

tan(beta)=2sin(beta)
sin(beta)/cos(beta)=2sin(beta)

sin(beta) cancels itself out on both sides

1/cos(beta)=2
1=2cos(beta)
cos(beta)=1/2
beta=arccos(1/2)

beta=pi/3 or 60 degrees

Answer 4

since tan b = sin b/cos b

therefore we have sin b/cos b = 2 sin b
(divide both sides by sin b and multiply both sides by cos b)
so 1 = 2 cos b
therefore b = angle whose cos is 1/2
or b = 60 degrees

Answer 5

sin ß / cos ß = 2 sin ß

As an earlier answer said.

Don't be tricked into dividing by 0!

EITHER sin ß = 0 OR
1 / cos ß = 2

Answer 6

(I'm switching the angle to x, I'm lazy, sorry ;)

I would divide both sides by 2sin(x)

1/2 = cos(x)
x = pi/3

Then check
tan(pi/3) = 2sin(pi/3)
[rt(3)/2]/[1/2] = 2(rt(3)/2)
rt(3) = rt(3)

so yes, pi/3 for the angle.

P.S. Don't forget to check the other quadrants, though. In the original equation, 5pi/3 also works

tan(5pi/3) = 2sin(5pi/3)
-sqrt(3) = -sqrt(3)

Answer 7

dividing both sides on 2sin(beta)
0.5=cos(beta)
beta=60
or beta = 300

Answer 8

sin ß / cos ß = 2 sin ß

you can eliminate the sin ß since they are both in the numerator

1/cosß = 2
cos ß = 1/2

ß = 60º

Answer 9

tan(b)=sin(b)/cos(b)=2sin(b) or

1/cos(b)=2 -> cos(b) = 1/2

so b = 60 deg

check tan(60)=1.732=2xsin(60) - checked

Answer 10

tanβ = 2sinβ

sinβ/cosβ = 2sinβ

So sinβ = 2sinβcosβ

ie sinβ - 2sinβcosβ = 0

ie sinβ( 1 - 2cosβ) = 0

So sinβ = 0 or 1 - 2cosβ = 0

ie sinβ = 0 or cosβ = ½

Solving for 0 ≤ β ≤ 2π (360°)

So β = 0, π , 2π or β = π/3, (2π - π/3)

ie β = 0, π/3 (60°), π (180°), 5π/3 (300°) , 2π (360°)

Check:

When β = 0, π, 2π

sinβ = tanβ = 0 so tanβ = 2sinβ yessssssssss!!!!!!!!!!

When β = π/3, tanβ = √3 and sinβ = √3/2 so tanβ = 2sinβ

yessssssssssssssssssssssssssssss!!!!!!

When β = 5π/3, tanβ = -√3 and sinβ = -√3/2 so tanβ = 2sinβ

yessssssssssssssssssssssssss!!!!!!!!!!!!!!!!!!!