TAF-2+Double+Angle+Formulas

TAF-2 Double Angle Formulas

This section will teach how to use double angle formulas to your advantage when trying to simplify complicated trigonometric expressions. Many functions involving powers of sine and cosine are hard to integrate. The use of Double-Angle formulas help reduce the degree of difficulty. There is only one equation for the sine double-angle formula and only one equation for the tangent double angle formula, but there are three cosine double-angle formulas. Sine Double-Angle Formula: sin(2A)=2sinAcosA Cosine Double- Angle Formulas: 1. cos(2A)=cos^2Asin^2A 2. cos(2A)=2cos^2A-1 3. cos(2A)=1-2sin^2A Tangent Double-Angle Formula: tan(2A)= 2tanA/1-tan^2A

Links: http://www.intmath.com/analytic-trigonometry/3-double-angle-formulas.php http://www.sosmath.com/trig/douangl/douangl.html

iMovie: media type="file" key="TAF-2 Sarah Muroski.mov" Sample Problem: Simplify: 1-2sin^•3w 1-2sin^2A=cos(2A) cos(2•3w)=cos6w

Verify: sinß=-1/8 270º≤ß≤360º fourth quadrant, draw triangle cos= (3√7)/8 sin2A=2sinAcosA =2(-1/8)(3√7/8) =2(-3√7/64) =-6√7/64=-3√7/32