Grade 12 Advanced Functions (Trigonometry) Questions?

1) cos of sin of x is bigger. The proof is

http://www.qbyte.org/puzzles/p109s.html

presuming x is real.

2) cos5x = cos^5x -10cos^3xsin^2x + 5cosxsin^4x

what does ^5x mean?

if its cos(x)^5, then yes, the other two methods work

cos(A + B) = cos A cos B - sin A sin B

cos(3x+2x)=cos3xcos2x-sin3xsin2x

cos3x=cos^3X - 3 cosX sin^2X

and it works from there.

Email me if you need more work/explanation for either,

Mackler

1. cossinx is bigger. Graph it.

2. cos(2x + 3x) Simplify that and keep simplifying using the addition and subtraction formulas

1) The way to do this is to use sin(x) = cos(pi/2 - x)

which gives you cos(pi/2 - cos x) vs. cos(sin x).

you can then use the identity cos(x) - cos(y) = -2sin(0.5x + 0.5y)sin(0.5x-0.5y)

to prove that cos(sin x) - cos(pi/2 - cos x) > 0 for all x

2) Here you need to use the rule cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

and the rule sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

with x = x and y = 4x