Question 341400
I'm assuming you can use your calculator.


Sin^-1 (-1/2) would be equivalent to sin^-1 (-.5).


Enter -.5 in your calculator and get Sin^-1 of it.


That should be equal to -30 degrees.


Tan (Tan -1 (1/2)) should be equal to 1/2 since you are finding the degree that has a tangent of 1/2 and then you are finding the tangent of that degree.


Follow it through with your calculator.


Tan^-1 (1/2) is the same as Tan^-1 (.5).


Enter .5 in your calculator and get Tan^-1 of it.


That should be equal to 26.56505118 degrees.


Put that in your calculator and get the Tan of it.


That should be equal to .5


If Sin(x) = y, then Sin^-1 (y) = x
If Cos(x) = y, then Cos^-1 (y) = x
If Tan(x) = y, then Tan^-1 (y) = x


These are inverse functions of each other.


This is no different then if {{{x^y = z}}}, then {{{z^(1/y) = x}}}


Put number into that equation to see how it works.


{{{2^6 = 64}}}
{{{64^(1/6) = 2}}}


Note that {{{64^(1/6)}}} is the same as {{{root(6,64)}}}


The exponents are being clipped.


They should be {{{1/y}}} and {{{1/6}}} respectively, depending on whether the denominator of the fractional exponent is a y or a 6.