MASTERSHEET 
Copy/Paste Formulae for Chapter 14 Circular Functions

>Copy the formula you need
>Paste it into the other workbook you are using
>NOTE: Do NOT alter the formulae in this workbook, these are your templates only.

Handy Shortcuts

Shift+Enter to execute a command
Ctrl-s save your file
Alt+7 to start a text cell
Ctrl-/ gives a fraction (□/□)
Ctrl-2 gives a square root sign (Sqrt[□])
Ctrl-6 gives an exponent (□^□)

All Mathematica commands start with a Capital and use square brackets [ ]
For examples Plot [ ]

MATHEMATICA COMMANDS FOR Chapter 14

1. Solve Equations

Solve["Left side of Equation"=="Right side of Equation","solve for"]

Solve[T==17-8Cos[Pi*5/12],T]

Solve[2x==8,x]//N

2. Solve Trig Equations with a range required

Solve[{"Left side of Equation"=="Right side of Equation","Lower range"<x<"Higher range"}]

Solve[{Tan[x]==1,0<x<2 Pi}]

3. Solve Simultaneous Equations

Solve[{equation here number one,another equation here},{variable1,variable2}]

Solve[{2x+3y==6,x-2y==4},{x,y}]//N

4. To plot one graph

Plot[{"function"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{2^x},{x,0,10},PlotLegends->"Expressions"]

5. To plot few graphs on the same plane

Plot[{"function1","function2","function3"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,2Pi},PlotLegends->"Expressions"]

6. Solve Inequalities

Reduce["Left side of the inequality""inequality sign here""Right side of the inequality","solve for",Reals]

Reduce[(72+15z)/3>4,z,Reals]

7. Complete the square

a:={"Enter the value for a here"}
b:={"Enter the value for b here"}
c:={"Enter the value for c here"}
Print["CompleteThe Square=",a(((x+(b/(2a))))^2)+(c-((b^2)/(4a)))]

a:={1}
b:={4}
c:={4}
Print["CompleteThe Square=",a(((x+(b/(2a))))^2)+(c-((b^2)/(4a)))]

8. Find an Exponential model

data={{"Enter first pair of data herewith comma in between(x1,y1)"},{"Enter first pair of data herewith comma in between(x2,y2)"},{"Enter first pair of data herewith comma in between(x3,y3)"},{"Enter first pair of data herewith comma in between(x4,y4)"},{"Enter first pair of data herewith comma in between(x5,y5)"}};
model=a ×(b^t);
fit=FindFit[data,model,{a,b},t]
modelf=Function[{t},Evaluate[model/.fit]]
Plot[modelf[t],{t,0,6},Epilog->Map[Point,data]]

data={{0.0,1.5},{2.0,0.5},{4.0,0.17},{5.0,0.09},{10.0,0.006}};
model=a ×(b^t);
fit=FindFit[data,model,{a,b},t]
modelf=Function[{t},Evaluate[model/.fit]]
Plot[modelf[t],{t,0,6},Epilog->Map[Point,data]]

9. Converting angles from radians to degrees

FullSimplify["Enter radian value here"/Degree]

"Angle in rads"*(180/π)

"Angle in degs"*(π/180)

FullSimplify[0.6/Degree]

10. Trig Function evaluation (If it is not degrees, cancel the DEGREE word in the command)

Cos["Enter degrees here" Degree]

or

FunctionExpand[Sin["Enter degrees here"Degree]]

Sin["angle in rads"]
Cos["angle in rads"]
Tan["angle in rads"]//N

Sin[Pi/3]

Cos[30 Degree]

FunctionExpand[Sin[-1.9]]

FunctionExpand[Sin[1.9Degree]]

11. Inverse Trig Function evaluation

ArcSin["Enter the trig value here"]

ArcSin[1]

12. Complete the square, Vertex ( Turning point), axis intercept

Manipulate[

d=b^2-4a c;
Pane[
Column[{
If[
a==0,
If[
b==0,
If[
c==0,
Plot[0,{x,-5,5},PlotRange->5,ImageSize->{200,200},PlotStyle->{Thick,Green}],
Plot[c,{x,-5,5},ImageSize->{200,200},PlotRange->5]
],

Plot[b x+c,{x,-5,5},PlotRange->5,ImageSize->{200,200},Epilog->{PointSize[.02],Green,Point[{{-c/b,0}}]}
]
],
(* else a!= 0 *)
Plot[a x^2+b x +c,{x,-5,5},PlotRange->5,ImageSize->{200,200},Epilog->{PointSize[.02],Green,
If[
d>=0,
{
Point[{{(-b+Sqrt[d])/(2a),0},{(-b-Sqrt[d])/(2a),0}}]

},
{}
],Red,Point[{-b/(2a),-b^2/(4a)+c}]}]
],

Text@Style[Grid[{{

If[
a==0,
TraditionalForm@Column[
{
Row[{"a"," = ",0,", so the function is not quadratic and there is no square to complete."}]
},Alignment->{Left,Top},ItemSize->{{18},Automatic}
],
(* else a != 0 *)
If[
b==0,
TraditionalForm@Column[
{
Row[{"b"," = ",0,", so the square is already complete."}]
},Alignment->{Left,Top},ItemSize->{{18},Automatic}
],
(* else b != 0 *)
row1=Row[{a (x^2)+b x,If[c>0," + "," "],If[c!=0,c," "]," ="}];
row2=Row[{a( (x^2)+b/a x),If[c>0," + "," "],If[c!=0,c," "]," ="}];
row3=Row[{a( (x^2)+2b/(2a) x+(b/(2a))^2),If[c-b^2/(4a)>0," + "," "],If[c-b^2/(4a)!=0,c-b^2/(4a)]," ="}];
row4=Row[{a(x+b/(2a))^2,If[c-b^2/(4a)>0," + "," "],If[c-b^2/(4a)!=0,c-b^2/(4a)," "]}];
Text@TraditionalForm@Column[First/@Split[{row1,row2,row3,row4}],Alignment->{Left,Top},ItemSize->{{18},{3,3,3,3}}]
]
],

If[
a==0,
Column[{""},ItemSize->{{18},Automatic}],
(* else a!=0 *)
TraditionalForm@Column[{
Text@TraditionalForm@Row[{"The vertex is at ",RawBoxes["("],-b/(2a),,", ",-b^2/(4a)+c,RawBoxes[")"]}],
Text@TraditionalForm@
Row[{"The ",If[d>=0,"real","complex"]" roots are \n",x," = ",
If[
d>=0&&IntegerQ[Sqrt[d]/(2a)],
Row[{-b/(2a)+Sqrt[d]/(2a)," and ",-b/2a-Sqrt[d]/(2a)}],
Row[{-b/(2a),If[Abs[Sqrt[d]/(2.a)]>0," +- "," -+ "],Abs[Sqrt[d]/(2a)]}]
] ,
If[d>=0,"",Row[{" ",I}]],"\n   ~~ ",
If[d>=0,
Row[{
NumberForm[(-b+Sqrt[d])/(2.a),{5,3}],
" and ",
NumberForm[(-b-Sqrt[d])/(2.a),{5,3}]
}],
(* else d<0 *)
Row[{
NumberForm[-b/(2.a),{5,3}],
If[
Abs[Sqrt[d]/(2.a)]==0,
"",
Row[{
If[Abs[Sqrt[d]/(2.a)]>0," +- "," -+ "], NumberForm[Abs[Sqrt[d]/(2.a)],{5,3}]," ",I
}]
 ]
}]
],
"."}]
},Alignment->{Left,Top},ItemSize->{{18},{3,6,7}}]
]
}},Alignment->{Left,Top}],16]
},Center]
,ImageSize->{575,400}],
{a,-3,3,1/10,Appearance->"Labeled"},
{b,-3,3,1/10,Appearance->"Labeled"},
{c,-3,3,1/10,Appearance->"Labeled"},
TrackedSymbols->Manipulate
]