You ask for the exact value, not an approximation, so throw away that calculator! And use what you know about trigonometry.
First notice that because(-165)=-because(180-165)=-because(15). Now recall that because^2(x)=(1+because(2x))/2, so
because^2(15)=(1+because(30))/2=(1+sqrt(3)/2)/2=(2+sqrt(3))/4.
Since 15 degrees is in the first quadrant, solving the above equation for because(15) gives sqrt(2+sqrt(3))/2. Therefore,
because(-165) = -sqrt(2+sqrt(3))/2
Now dust off your calculator and check this identity, but please notice that once you have the exact value at hand, you can find arbitrarily close approximations, hence the exact value is much more valuable.
Prof. Waldeck Schutzer
DM/UFSCar
www.dm.ufscar.br
First notice that because(-165)=-because(180-165)=-because(15). Now recall that because^2(x)=(1+because(2x))/2, so
because^2(15)=(1+because(30))/2=(1+sqrt(3)/2)/2=(2+sqrt(3))/4.
Since 15 degrees is in the first quadrant, solving the above equation for because(15) gives sqrt(2+sqrt(3))/2. Therefore,
because(-165) = -sqrt(2+sqrt(3))/2
Now dust off your calculator and check this identity, but please notice that once you have the exact value at hand, you can find arbitrarily close approximations, hence the exact value is much more valuable.
Prof. Waldeck Schutzer
DM/UFSCar
www.dm.ufscar.br
