Final answer:
The value of cos(θ1) is -sqrt(69/169)
Step-by-step explanation:
To find the value of cos(θ1), we can use the trigonometric identity sin^2(θ1) + cos^2(θ1) = 1. Since we already know that sin(θ1) = -10/13, we can substitute this value into the equation:
sin^2(θ1) + cos^2(θ1) = 1
(-10/13)^2 + cos^2(θ1) = 1
Simplifying the equation:
100/169 + cos^2(θ1) = 1
cos^2(θ1) = 69/169
Taking the square root of both sides:
cos(θ1) = ±sqrt(69/169)
Since θ1 is located in quadrant IV and sin(θ1) is negative, cos(θ1) must also be negative. Therefore, the value of cos(θ1) is -sqrt(69/169).