--> Produced by MATCAL Program
--> Solving for the roots of the sinosodial(trig) equation
--> 5TanXCosX -8CosX = 4 , Eq(1)
--> Using the trigonometrical identities
--> Tan(A) = Sin(A) / Cos(A)
--> Replace Tan(A) with the identity above to eliminate the
Tan(A)
--> 5Sin(A) / Cos(A) x CosX -8CosX = 4 , Eq(1)
--> Divide the right side by Cos(A) to reduce the fraction
--> 5Sin(A) x -8CosX = 4 , Eq(1)
--> Move the -8Cos(A) to the right side , Eq(1)
--> 5Sin(A) x = 4 + 8CosX , Eq(2)
--> From the identity table , Sin(A)^2 + Cos(A)^2 = 1 , and
Sin(A) = Sqrt( 1 - Cos(A)^2 )
--> Replace the Sin(A) in the Eq(2) with the identity in Eq(3)
--> 5Sqrt( 1 - Cos(A)^2 ) = 4 + 8CosA , Eq(4)
--> Square both sides of the equation to eliminate the radical on
the right hand side
--> 5^2( 1 - Cos(A) )^2 = ( 4 + 8CosA )^2 , Eq(4)
--> 25( 1 - Cos(A) ) = ( 4 + 8CosA )^2 , Eq(4)
--> 25( 1 - Cos(A) ) = ( 4 + 8CosA ) x ( 4 + 8CosX ) , Eq(4)
--> 25 -25Cos(A) = 16 + 32Cos(A) + 32Cos(A) + 64Cos(A)^2 ,
Eq(4)
--> Combine all like terms together
--> 25 -25Cos(A) = 16 + 64Cos(A) + 64Cos(A)^2 , Eq(4)
--> 0 = -9 + 64Cos(A) + 89Cos(A)^2 , Eq(4)
--> 0 = 64Cos(A)^2 + 89Cos(A) -9 , Eq(4)
--> 64Cos(A)^2 + 89Cos(A) -9 = 0 , Eq(4)
--> Let Y = Cos(X) , and Y^2 = Cos(A)^2
--> 89Y^2 + 64Y -9 = 0 , Eq(4)
--> Solve for the zero(s)/roots of the equation using the
quadratic formula
--> Solve for the value of X using quadratic formula
--> The quadratic formula is X = (-b (+&-1) Sqrt(b^2 - 4ac) ) / 2a
--> 89Y^2 + 64Y -9 = 0 , Eq(4)
--> a = 89 , b = 64 c = -9
--> Y = - 64 + Sqrt(64^2 - 4 * 89 * -9) / 2 * 89
--> Y = - 64 - Sqrt(64^2 - 4 * 89 * -9) / 2 * 89
--> Y = - 64 + Sqrt(4096 - 4 * -801) / 2 * 89
--> Y = - 64 - Sqrt(4096 - 4 * -801) / 178
--> Produced by MATCAL Program
--> Y = - 64 + Sqrt(4096 - 4 * -801) / 178
--> Y = - 64 - Sqrt(4096 - 4 * -801) / 178
--> Y = - 64 + Sqrt(4096 + 3204) / 178
--> Y = - 64 - Sqrt(4096 - 3204) / 178
--> Y = - 64 + Sqrt(7300) / 178
--> Y = - 64 - Sqrt(7300) / 178
--> Y = - 64 + (85.4400374531753) / 178
--> Y = - 64 - (85.4400374531753) / 178
--> Y = 21.4400374531753 / 178
--> Y = -149.440037453175 / 178
--> Tan(A) = 0.120449648613344
--> Tan(A) = -0.83955077220885
--> Tan(A) = (Root/zero) = 0.12
--> Tan(A) = (Root/Zero) = -0.84
--> Tan(A) = (Root/zero) = 0.12
--> Tan(A) = (Root/Zero) = -0.84
-- > The are two solutions for the function to exist which are .
--> Tan(A) = (Root/zero) = 0.12
--> Tan(A) = (Root/Zero) = -0.84
--> A = ArcTan (0.12)
--> A = Arctan (-0.84)
--> A = 6.84002030832302
--> A = -40.0141535976838
--> Angle(A) = 6.84
--> Angle(A) = -40.01
--> Cos(A) = 0.12
--> A = ArcCos(0.12)
--> Angle(A) = 83.0744599974608
--> Angle(A) = 83.07
--> A = ArcCos(-0.84)
--> Angle(A) = 147.080919634093
--> Angle(A) = 147.08
--> Produced by MATCAL Program
--> Checking Process / Stages
--> 5TanXCosX -8CosX = 4 , Eq(1)
--> 5 x Tan83.0744599974608Cos83.0744599974608
-8Cos83.0744599974608 = 4 , Eq(1)
--> 5 x 8.27311576399391 x 0.12 -8 x 0.12 = 4 , Eq(1)
--> 5 x 8.27311576399391 x 0.12 -8 x 0.12 = 4 , Eq(1)
--> 4.00386945839634 = 4 , Eq(1)
--> 4.00 = 4 , Eq(1)
--> Produced by MATCAL Program
15 - Circle Of Life.mp3
Felix liberty one life to live.mp3
