find sin2x, cos2x, and tan2x if sinx= 3/sqrt13 and x terminates in quadrant I

Question

find sin2x, cos2x, and tan2x if sinx= 3/sqrt13 and x terminates in quadrant I

Answer 1

Hi Justin,

 

sinx = 3/sqrt(13) and x is in the first quadrant. This means all the values of the functions are positive.

Find the angle x using arcsin(3/sqrt(13)) = x.

Find the length of the other side using the Pythagorean Theorem using the information from sin x = 3/sqrt(13).

Once you find these, you have all the info to solve the problem. For example, to find sin2x, you will multiply x by 2 and then find its sin.

Alternatively, you can use the angle sum and difference identities such as cos(x+y) = ...., sin(x+y) = .... by repacing y with x.