Question

How do you find sin^-1 (-1)
(Inverse Trig Functions)

Answer 1

Sine of what angle produces -1?

Answer 2

a calculator will tell you. But in this case you should have memorized a few important angles and their sin, cos and tan

sin(0) = 0
sin(30) =1/2
sin(45) = sqrt(2)/2
sin(60)= sqrt(3)/2
sin(90)= 1

then you need to know about the 4 quadrants (quadrant 2 is 90 to 180, Q3 is 180 to 270, Q4 is 270 to 360)

Answer 3

How about this. Where on the unit circle is the y value -1?

Answer 4

That would be at 270 degrees.

Answer 5

@phi, I know the calc will, but I don't think thats the way he wants us to do it.

Answer 6

You might think so, 270º, but that is not in the Range of the Inverse Sine Function.

Answer 7

Right, the range is from positive pi over two to neg.

Answer 8

Good call. -90º or -pi/2.

Answer 9

Wait, I thought that 90 degrees to 270 degrees was the same as positive pi/2 to negative pi/2 on the unit circle. Why wont 270 work?

Answer 10

-90º = -pi/2 -- This is IN the Range of the Inverse Sine Function
270º = 3pi/2 -- This is NOT in the Range of the Inverse Sine Function

Answer 11

Where is -90 and 90 degrees on the unit circle? Because our teacher had us label this unit circle from 90 which is at the top to 270 degrees, 180 from 90 degrees going clockwise.

Answer 12

and that was supposingly the limit of sine

Answer 13

That is right,

90º = pi/2 -- This is the top of the unit circle.

270º = 3pi/2 is the bottom of the unit circle, but in the anti-clockwise direction from the top.

-90º = -pi/2 is the bottom of the unit circle in the clockwise direction from the top.