Question

sin theta= tan theta

Answer 1

solve for theta?

Answer 2

solve the trig equation 0<theta<2pi

Answer 3

I replace theta =x for easy following
sin x - tan x =0
\[sinx -\frac{sinx}{cosx}=0\]
\[\frac{sinxcosx-sinx}{cosx}=0\]
\[\frac{sinx (cosx -1)}{cosx}=0\]
\[sinx =0 \]\[cosx -1=0\]
\[sinx =0-----> x = 0 ; x = pi\]
\[cosx -1=0 ----> cosx =1 ---> x = 0 ; x = 2pi\]
therefore: x=0, x = pi and x =2pi are solutions

Answer 4

nope, no mistake

Answer 5

sin2xsinx=cosx

Answer 6

what is it? the new one?

Answer 7

yes

Answer 8

sin2x = 2sinx cos x therefore
2sinxcosxsinx -cosx =0
cosx (2sin^2 x -1)=0
cos x =0 ---> x = pi/2 or 3pi/2
2sin^2x -1 = 0 ---> 2sin^2 x=1 ---> sin^2x = 1/2 ---> sin x = sqrt (1/2)
x = pi/4 or 3pi/4

Answer 9

no more, friend

Answer 10

thank you so much!!