Question

How do you evaluate the sine, cosine, and tangent of the angle 53 degrees without using a calculator?

Answer 1

I would try using a thing called expansion in series:

Explanation:

Basically the value of your trigonometric function is found simply adding terms that are easy to manipulate (each term is a fraction involving your angle in radians that is "easy" to evaluate).

You first need to consider your angle in radians:
`x=53^o=0.9250 rad`

Than you use these expansions for `sin` and `cos` and the relationship between them and `tan` as:

Using them you get:

Hope it helps!