Question

For 0°≤θ<360°, how many roots does the equation tanθ+2sinθ=0 have?

Answer 1

tan(x) + 2*sin(x) = 0

sin(x)/cos(x) + 2*sin(x) = 0

sin(x)( 1/cos(x) + 2 ) = 0

sin(x) = 0 or 1/cos(x) + 2 = 0

I'll let you finish up

Answer 2

is it 3?

Answer 3

no

Answer 4

sinx=0 has 2 roots right?

Answer 5

cosx=-1/2.....
4?

Answer 6

yes

if sin(x) = 0, then x = 0 or x = 180

Answer 7

1/cos(x) + 2 = 0

1/cos(x) = -2

cos(x) = -1/2

x = 120 or x = 240

Answer 8

So there are 4 solutions in the interval 0 <= x < 360

Answer 9

ohh, yes, thank you

Answer 10

yw

Answer 11

and which of the following equations has/have solutions?
A. 2cos^(2)θ-sin^(2)θ=1
B. 2cos^(2)θ-sin^(2)θ=2
C. 2cos^(2)θ-sin^(2)θ=3

Answer 12

Your best bet is to graph each of them

if the equation has x-intercepts, then the equation has solutions