Find sin(tan^-1((sq root of 3)/3)? Find the exact value of cos(sin^-1(11/61))? Find cos(sin^-1(-0.25))?

1. Find sin(tan^-1((sq root of 3)/3)?


2. Find the exact value of cos(sin^-1(11/61))?


3. F ind cos(sin^-1(-0.25))?





Homework Help please

Find sin(tan^-1((sq root of 3)/3)? Find the exact value of cos(sin^-1(11/61))? Find cos(sin^-1(-0.25))?
1.


first look at the tan^-1((sq root of 3)/3 part


it is asking what angle of tan will give you (sqrt3)/3


and the angle is pi/3


tan^-1((sq root of 3)/3 = pi/3





so now you got sin(pi/3) = (sqrt3)/2





2.


sinx = opposite/hypotenuse


draw a triangle and put a theta, then put 11 on the opposite side and 61 as the hypotenuse.


use pythagorean theorem to find the adjacent length


61² = 11²+b²


b=60





so cos of that angle will be adjacent/hypotenuse which will be 60/61





3.


do the same as number2