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!
Hello OVechkin8What 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?
Grandad
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