Today in Math...

So.. today in math we learned more TRIG. We're now learning Chapter 7 Section 5, Multiple-Angle and Product-to-Sum Formulas. We Use the unit circle above to find all the solutions. There are like a million formulas to memorize!! The test is next week!!

Solving a multiple-angle equation

*Note* :

(2) means squared

(pie) is a replacement for the symbol pie

Double Angle Formulas:

sin 2u= 2 sin u cos u

tan 2u= (2 tanu)/(1- tan2u)

cos 2u= cos2u - sin2u

= 2 cos2u - 1

= 1- 2sin2u

Solve: 2 cos x + sin 2x = 0

2 cos x + sin 2x = 0 Write the original equation

2 cos x + 2 sinx cosx = 0 Substitute into the double- angle formula

2 cos x (1 + sin x) = 0 factor out 2 cos x

2 cos x = 0 and 1 + sin x = 0 set the factors equal to zero

x = (pie)/2, 3(pie)/2 x = 3(pie)/2 The solutions in [0,2(pie))

The general solution is...

x = (pie)/2 + 2n(pie) and x = 3(pie)/2 + 2n(pie)

where n is an integer.

That is only a portion of what I learned in math...