Help with precal please

Question

anonymous · Answer

hi Welcome to Openstudy!

got any specific problem that we can work on?

anonymous · Answer

Thank you!  I need help with solving trigonometric equations.

tanxcosx = 1/2

freckles · Answer

tan(x)=sin(x)/cos(x) right?

anonymous · Answer

tan(x) times cos(x) = 1/2 (0.5)

anonymous · Answer

I know you have to start by changing tanx into terms of sin and cos so would tan equal sin over cos?

freckles · Answer

$$\frac{\sin(x)}{\cancel{ \cos(x) }} \cancel{ \cos(x) }=\frac{1}{2}$$

anonymous · Answer

Thank you!

freckles · Answer

Now you refer to the unit circle. 
You look for angles x such that sin is 1/2 (look for when the y-coordinate is 1/2)

anonymous · Answer

I've got it from here! Thank you very much

freckles · Answer

np

anonymous · Answer

Is this correct?

2sinx + 1 = 0
           -1     -1
2sinx = -1

*divide both sides by 2*
sinx = -1/2

and then so on with the unit circle

anonymous · Answer

yes it's right (:

anonymous · Answer

help!
2cosx + square root of 3 = 0

freckles · Answer

Do the same thing you did above when you solve sin(x) in the equation 2sin(x)+1=0

anonymous · Answer

i first squared both sides to get rid of the square root of three and then divided both sides by 2 with that answer and that left me with cos^2x = 2 and now im stuck because there is no square root of 2

anonymous · Answer

you don't have to calculate the square root of both sides.

freckles · Answer

same thing you did above when solving for sin(x)
$$2\cos(x)+\sqrt{3}=0 \ 2\cos(x)=-\sqrt{3}$$

freckles · Answer

I leave that last step to you
which I think you know is to ..

anonymous · Answer

divide by 2! thank you

anonymous · Answer

help

$$\sqrt{2}sinx + 1 = 0$$

anonymous · Answer

same process as before,  but this you have to divide both sides by $\sqrt{2}$

anonymous · Answer

What is 0/ $$\sqrt{2}$$

anonymous · Answer

0?

anonymous · Answer

$\sqrt{2}sinx + 1 = 0\\sqrt{2}sinx=-1 $

anonymous · Answer

then divide both sides by $\sqrt{2}$

anonymous · Answer

So you get $$sinx = -1\div \sqrt{2}$$

anonymous · Answer

That's not an option on the unit circle

anonymous · Answer

conjugate the denominator and it will be equivalent to $\Large \frac{\sqrt{2}}{2}$

anonymous · Answer

oops forgot the negative sign

anonymous · Answer

$$2\cos ^{2}x = 1$$