Question

1. Whats the exact value of
cot[cot^-1 sqrt3/3] ?

( is it infinity? )


2. Whats the exact value of
sin^-1(cos pi/2) ?

( is it 0? )

3. Whats the exact value of
tan(sin^-1 x/2) ?

Answer 1

for the first one, at what angle is cotangent sqrt(3)/3

Answer 2

do you not understand your own homework?

Answer 3

at what angle is cotanget sqrt(3)/3?

Answer 4

Nope, thats why I need help... I don't understand it

60 degrees?

Answer 5

1. The arccot of sqrt(3)/3 is 60 degrees, or pi/3. The cot of pi/3 is once again sqrt(3)/3.
2. Cosine of pi/2 is cosine of 90 degrees. The x-value at 90 degrees is 0, so cos pi/2 is 0. Arcsine of 0 is 0.

Answer 6

tan(sin^-1 x/2)

Arcsine of x/2 will give you a certain angle, theta. We can draw a right triangle off this. Sine is opposite over hypotenuse.Tangent is opposite over adjacent. So tangent of theta is \[\tan \theta = \frac {x}{\sqrt {4-x^2}}\]