Question

For 0°≤θ≤360°, how many roots does the equation tanx=2sinx have?

Answer 1

start with writing \(\tan \theta\) as \(\frac{\sin \theta}{\cos \theta}\)

Answer 2

yup

Answer 3

u droped some of solutions with canceling \(\sin x\)

Answer 4

sinθ/cosθ = 2sinθ
sinθ/2sinθ = cosθ
1/sinθ=cosθ ??

Answer 5

ok see u have\[\frac{\sin x}{\cos x}=2 \sin x\]multiply by \(\cos x\)\[\sin x=2\sin x \cos x\]\[\sin x-2\sin x \cos x=0\]\[\sin x(1-2 \cos x)=0\]now use zero product property

Answer 6

makes sense?

Answer 7

sinx=0
x=0,180,360

Answer 8

1-2cosx=0
cosx=-1/2 ?

Answer 9

x=120?

Answer 10

be careful :) \[\cos x=\frac{1}{2}\]ha? :)

Answer 11

oops

Answer 12

60?

Answer 13

just 60 ?

Answer 14

300?

Answer 15

right :)

Answer 16

5 roots?

Answer 17

quite right :)

Answer 18

thanks

Answer 19

welcome :)