# Sin/cos/tan by hand?

#### Goliatbagge

Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?

Gold Member

#### jasonRF

Gold Member
Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?
Of course you will turn these into radians ... but since all of your values are near $\pi/4$, I would use,
$$\sin ( \pi/4 + x) = \sin(\pi/4) \cos(x) + \sin(x) \cos(\pi/4) = \left(\cos(x) + \sin(x) \right) / \sqrt{2}.$$
Your values of $x$ are $-\pi/180, -2 \pi/180, - 3 \pi/180, ...$ which are small, so you can take the first few terms in the Taylor series for sin and cos near zero. Even approximating $\cos(x) \approx 1$ and $\sin(x)\approx x$ should get you several correct digits for the exact examples you gave.

jason