Question

*Trigonometric Functions*
What is the solution of this equation over the interval [0,2pi]: cos(x)tan(x)-1/2=0?
*help is appreciated and will give medal*

Answer 1

what's the reciprocal of tan ?

Answer 2

good job princess

Answer 3

sec?

Answer 4

no cos =1/sec and sin=1/csc tan =what ?
what's the definition of tan how would you write tan in terms of sin cos ?

Answer 5

what ? sec ? lol

Answer 6

Cas1 is a skank retricewhore

Answer 7

lol no one knows

Answer 8

lol be quiet @chafrees1 i love u bruh

Answer 9

tan x° = Opposite / Adjacent?

Answer 10

relation between trig functions

Answer 11

Thank you I see now.

Answer 12

tan = sin/cos
\[\rm \cos(x)\color{ReD}{ \tan(x)}-\frac{1}{2}=0\]
replace tan with sin/cos and then simplify it

Answer 13

your welcome

Answer 14

cos(x)sin(x)/cos(x)-1/2=0?

Answer 15

\[\huge\rm \cos(x)*\frac{\sin(x)}{\cos(x)}-\frac{1}{2}=0\]
which is same as \[\frac{ \cos(x)*\sin(x) }{ \cos(x)}-\frac{1}{2}=0 \]

Answer 16

Ok I see

Answer 17

simplify that

Answer 18

x=π6±2πn,5π6±2πn?

Answer 19

hamm what's that ?
what would be the next step ?
\[\frac{ \cos(x)*\sin(x) }{ \cos(x)}-\frac{1}{2}=0 \]

Answer 20

to multiply cos(x) and sin(x)?

Answer 21

i already did part now cos(x) times sin (x) over cos(x) = ??

Answer 22

I don't know I'm stuck on this part

Answer 23

let cos(x) = y
and sin(x) = z
\[\color{Red}{\frac{ \cos(x)*\sin(x) }{ \cos(x)}}-\frac{1}{2}=0 \]
\[\color{Red}{\frac{ y*z}{ y}}-\frac{1}{2}=0 \]

Answer 24

\[\rm \frac{ y*z }{ y }=??\]

Answer 25

yz/y?

Answer 26

ye correct what else ? simplify that

Answer 27

z is all that's left?

Answer 28

right and we supposed that z=sin(x)
same thing let cos(x) = y
and sin(x) = z
\[\color{Red}{\frac{ \cancel{\cos(x)}*\sin(x) }{ \cancel{\cos(x)}}}-\frac{1}{2}=0 \]
\[\sin(x)-\frac{1}{2}=0\]
now jsut solve for sin(x)

Answer 29

sin(x) is z?

Answer 30

so z=1/2?

Answer 31

well i just replaced sin(x) with z to make it looks easy

Answer 32

yes right so sin(x) = 1/2 now u can use unit circle to find exact solution from 0 to 2pi

Answer 33

(x,y) order pair where x-coordinate =cos
and y-coordinate = sin

Answer 34

(1,0)?

Answer 35

no sin(x)=1/2 you have to find x value at what angle sin(x) is 1/2 ?