Practice with trig functions:
In these problems a^b denotes a raised to the power b.
So sin^2(x) means to square the sin of x.
Use the double angle formulae to show:
- tan(x) sin(2x)=2sin^2(x)
- sin(2x)/(1+cos(2x))=tan(x)
- 2tan(x)/(1+tan^2(x))= sin(2x)
Use the addition formulae to show:
- sin(a+b)+sin(a-b)=2sin(a)cos(b)
- sin(c)+sin(d)=2sin((c+d)/2)cos((c-d)/2)
(Hint: let c=a+b and let d=a-b)
Use the addition formulae to write
- 4 cos(x) + 3 sin(x) in the form c sin(x+b) then graph your result.
- 4 cos(x) - 3 sin(x) in the form d cos(x+e) then graph your result.
Problems similar to the last two were done in class: first draw a
right triangle with legs 3 and 4, then rewrite the legs in terms of the
sine and cosine of one of the acute angles.
Sean Watson has created another list of practice problems along with
his suggestions for what to remember:
more practice!
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