Given the sine (or cosine) of an angle, find its cosine (or sine) using the Pythagorean identity.

Problem

The angle theta, start subscript, 1, end subscript is located in Quadrant I, V, and sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 13, divided by, 85, end fraction .
What is the value of cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Express your answer exactly.
cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals