SOLUTION: So, the instructions on the problem say: 'Use the identities to rewrite each expression in terms of a single trigonometric function. Check your result by graphing. {{{ 4sin^2(7t

Algebra ->  Trigonometry-basics -> SOLUTION: So, the instructions on the problem say: 'Use the identities to rewrite each expression in terms of a single trigonometric function. Check your result by graphing. {{{ 4sin^2(7t      Log On


   

Question 816020: So, the instructions on the problem say:
'Use the identities to rewrite each expression in terms of a single trigonometric function. Check your result by graphing.
+4sin%5E2%287t%29cos%5E2%287t%29+
I recognized that it has a similar form to sin2t= 2sintcost but the sin and cos are squared in this problem. What else can I do? Maybe transform the sin^2 or cos^2 to a different identity? Thank you so much, this is such a great site for help.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
+4sin%5E2%287t%29cos%5E2%287t%29+
Recognizing that the sin(2x) identity is buried in there is more than half the battle! Very good!

Now we just have to see how we can use it. Yes, the sin and cos in your expression are squared. But isn't 4 also the square of the 2? So isn't your expression just the square of sin(2x)?:
%282sin%287t%29cos%287t%29%29%5E2
Now we can use the sin(2x) formula with 7t in the place of x:
%28sin%282%287t%29%29%29%5E2
The argument simplifies:
%28sin%2814t%29%29%5E2
which can also be written as:
sin%5E2%2814t%29