1. ## [SOLVED] Trig Functions

Hello mates, I would like some help with these problems,

1. Solve tan(θ) + 1 = 0, 0 ≤ θ < 2pi

2. Solve tan(θ) − 3cot(θ) = 0, 0 ≤ θ < 2pi

3. Solve 2sin(θ) − √2tan(θ) = 0, 0 ≤ θ < 2pi

Have a great holiday break!

2. Hello OVechkin8
Originally Posted by OVechkin8
Hello mates, I would like some help with these problems,

1. Solve tan(θ) + 1 = 0, 0 ≤ θ < 2pi

2. Solve tan(θ) − 3cot(θ) = 0, 0 ≤ θ < 2pi

3. Solve 2sin(θ) − √2tan(θ) = 0, 0 ≤ θ < 2pi

Have a great holiday break!
What have you done to try to solve these?

#1 is very simple: $\displaystyle \tan \theta = -1$. So ...?

#2: $\displaystyle \tan\theta -\frac{3}{\tan\theta}=0$

$\displaystyle \Rightarrow \tan^2\theta - 3 = 0$

So ...?

#3: $\displaystyle 2\sin\theta -\frac{\sqrt2\sin\theta}{\cos\theta}=0$

$\displaystyle \Rightarrow 2\sin\theta\cos\theta -\sqrt2\sin\theta=0$

$\displaystyle \Rightarrow \sin\theta(2\cos\theta-\sqrt2)=0$

$\displaystyle \Rightarrow \sin\theta = 0$ or ...?

Can you complete these now?

3. ## check this out

1) tanx+1=0
tanx=-1
therfor
x=3pi/4 or 7pi/4

2)tanx-3cotx=0
tanx-3/tanx =0
(tanx)^2-3=0
tanx=+-(3)^(1/2)
therfor
x= pi/3 or 4pi/3 or 2pi/3 or 5pi/3
3) 2sinx-(sqrt2)tanx=0
2sinx=(sqrt2)tanx
2sinx=(sqrt2)sinx/cosx
cosx = 1/(sqrt2)
or sinx=0

therfor
either x=0 or
x=pi/4 or 7pi/4

4. Thanks guys, for the last one it was, 0, pi, pi/4, and 7pi/4. SOLVED.