SOLUTION: Hey, Tutor Thanks for taking the time to help me. I have a few questions about graphing sin and cos functions. If you could show me the process you used to graph these, it would b

Q1)  In your Q1, the formula has three opening parentheses and only two closing parentheses.

     So, your writing is UNREADABLE in this case. It CONTRADICTS to rules of Math grammar.



Q2)  y = sin(7x-2x) = simplify the expression in parentheses = sin(5x).

     So, it is similar to sin(x), but x-axis is compressed with the coefficient of 5.

     Due to this reason, in the interval [0,2pi] you have 5 complete periods of sine, instead of one.


     If you want to plot it (to produce a real plot/graph), you can make a table with the input
     of x values and the output of corresponding y-values; then plot each point on graph paper 
     and connect the points, using a pen. It is a standard way to get a sketch. This method is what the 
     young students learn somewhen in 4-th or 5-th grade. It is what on the line of knowledge 
     goes immediately after the multiplication table.


     Alternatively, you may go to website http://www.desmos.com/calculator

     There is free of charge plotting tool there, which will produce plots for you free of charge.
     You only need to print an equation of your function there.



Q3)  Here your writing is not standard; therefore, I can not read your writing: 

          is it  y = 2sin^2(x)-2  or  y = 2sin(2x)-2 ?



Q4)  You can find average of "two points" in the same as you find the average of any two quantities,
     does not matter of their dimensions (radians, degrees, kilograms, meters, degrees of temperature, 
     dollars, hours, and so on . . . )


                 Add the two numbers and divide the sum by 2; 
              then write the dimension next to the final number.


     So, using your example, 

         the average =  =  =  =   radians.    ANSWER



Q5)  Notice that sin(60 degrees) = sin(pi/3).

     Therefore,   -  =  -  = make standard operations with fractions =  -  =  -  = .