SOLUTION: Circle the Larger Number 1. a) tan^-1(-1/4) b) cos^-1(-1/4) 2. a) sin(4pi/5) b) cos(4pi/5)

Algebra ->  Trigonometry-basics -> SOLUTION: Circle the Larger Number 1. a) tan^-1(-1/4) b) cos^-1(-1/4) 2. a) sin(4pi/5) b) cos(4pi/5)      Log On


   

Question 609501: Circle the Larger Number
1.
a) tan^-1(-1/4) b) cos^-1(-1/4)

2.
a) sin(4pi/5) b) cos(4pi/5)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
1. a) tan^-1(-1/4) b) cos^-1(-1/4)
The range for tan^-1 is -pi%2F2 through pi%2F2. And since the argument is negative, tan^-1(-1/4) will have a value between 0 and -pi%2F2 (i.e. negative). The range for cos^-1 is 0 to pi. And since the argument is negative, cos^-1(-1/4) will have a value between pi%2F2 and pi. Positive is larger than negative.

2. a) sin(4pi/5) b) cos(4pi/5)
4pi%2F5 is in the second quadrant. sin is positive in the second quadrant and cos is negative in the second quadrant. Again, positive is larger than negative.