If tan theta 78 pi SolutionIn rt triangle ABC with B 90degr

Solution

In rt triangle ABC with B= 90degrees (draw figure)
If C is theta, tanC=7/8
i.e., AB = 7, BC = 8 (in simplest terms)
using pythagoras theorem, AC= sqrt(113) = 10.63

Now sinC = 7/10.63

cosC = 8/10.63

Then sin2C = 2*sinC*cosC = 2*56/10.63^2 = 0.991

cos2C = 2*cosC^2 - 1 = 0.133