# Math Help - Trig equation

1. ## Trig equation

2cos(3t-30deg)=-(square root of 2)
[0,360)

2. Hello,

If $t \in [0,360]$ then $3t \in [0,1080]$.

Hence $3t-30=X \in [-30,1050]$.

The problem is equivalent to finding X such as $2 \cos(X)=-\sqrt{2}$

$\cos(X)=-\frac{\sqrt{2}}{2}$

We know that if $\cos(X)=\cos(a)$ then the solutions are $\left\{X=a+360k; X=-a+360k \ / \ k \in \mathbb{Z} \right\}$

We know that $\cos(315)=\frac{-\sqrt{2}}{2}$

So find all solutions in $[-30,1050]$ according to what i've written just before

Then replace for t in X

3. {\sqrt{2}}{2}