I'm trying to learn how to calculate trig functions in my head. I'm planning on learning $\cos(x), x∈[0,π/2]$ and then using symmetry to calculate the others.

I think the quadratic Maclaurin series at $0$ and the linear at $π/2$ could be calculated in a matter of seconds with some practice. However, I'm struggling to find something that works to 2 D.P. on the interval $(0.7, 1.2)$.

My best idea so far is to use $\color{green}{ 1.3-x/1.3}$, but that is neither fast nor accurate to 2 D.P.

### Graph of $\color{red}{\cos(x)},\ \ \color{blue}{1-x^2/2},\ \ \color{green}{1.3-x/1.3},\ \ \color{blue}{π/2-x}$:

### Error:

How can I quickly approximate $\cos(x)$ for $x∈(0.7, 1.2)$? Or is there a better way to do this?