Evaluate the sine, cosine, and tangent of the angle without using a calculator. θ = - 10π 3

Determine the quadrant adding or subtracting periods - 10pi/3+2pi=-4pi/3+2pi=2pi/3

which is the second quadrant because

first quadrant is between 0 and pi/2

second quadrant is between pi/2 and pi

third quadrant is between pi and 3pi/2

fourth is between 3pi/2 and 2pi

now we find the terminal angle since it is the second quadrant we use theta'=pi-theta=pi-2pi/3=pi/3

sin (pi/3) = sqrt (3) / 2 sin is positive in the second quadrant

cos (pi/3) = - 0.5 cos is negative in the second quadrant

tan (pi/3) = sin (pi/3) / cos (pi/3) = - sqrt (3) tan is negative in the second quadrant