How to you find cos sin or tan of an angle in square root form with a calculator?

With the exception 0 degrees and the multiples of pi/2. All the sin x, and cos x when evaluated for a particular angle will give you an irrational number as the answer.

Since in Trig we are more interested in relationships among functions and not in evaluating a function, like tan 123 degrees,we use certain angles whose trig functions are well known. Like ( in degrees ) 0, 30, 45,60,90, etc

We have to remember than when we say that tan 60 = SQR ( 3) , we are not getting an exact answer; because if you change SQR (3) to a decimal, we get a never ending number.

My calculator gives me tan 60 = 1.732050808.... , and for SQR (3) = 1.732050808....

You can get the functions of angles commonly used like : 30,45,60, and their related angles using two different right triangle.

For function of 45 degree we used an isosceles right triangles whose legs are both 1 unit and the hypotenuse is 2 units

For the 30 - 60 triangle we use a right triangle whose side opposite to the 30 degrees angle is 1 a.s the opposite to the 60 angle is SQR (3);, the hypotenuse is 2 units.

Using trigonometric identities we can find exact ( irrational ) values for angles like 75 degrees ( using 30 + 45 ), for 15 degrees. ( 45 - 30 ), etc.

I hope this helps.

sin(x) = sqrt(sin(x)^2) providing sin(x)>0, so for example

sin(27°) = sqrt(0.2061073739)

Gnaw