Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewIf you know the formula from Problem 1 in this section you can get this one for free.( θ) + ( θ)=( θ)( θ)+ =( θ)( θ) ( θ)2 2tan ( θ) + 1 = sec ( θ)2 2sin cos 12 2sin cos 1cos cos cos2 2 222Can you come up with a similar formula relating cot ( θ ) and ( )3. sin ( 2t ) =Solutionsin 2t = 2sin t cos t( ) ( ) ( )csc θ ?This formula is often used in reverse so that a product of a sine and cosine (with thesame argument of course) can be written as a single sine. For example,( )( x ) ( x ) = ( x ) ( x )sin 3 cos 3 sin 3 cos 33 2 3 2 2 22( ( x ))⎛1 ⎞= ⎜ sin 2 3 ⎟⎝2⎠1 sin3 2= ( 6 x )8You will find that using this formula in reverse can significantly reduce thecomplexity of some of the problems that you’ll face in a Calculus class.334. cos( 2x ) =(Three possible formulas)SolutionAs noted there are three possible formulas to use here.2 2cos 2x = cos x − sin x( ) ( ) ( )2cos( 2x) = 2cos ( x)−12cos( 2x) = 1−2sin ( x)You can get the second formula by substituting sin 2 ( x) 1 cos2( x)from this section) into the first. Likewise, you can substitute cos 2 ( x) = 1−sin2( x)into the first formula to get the third formula.= − (see Problem 15.2cos ( x ) =(In terms of cosine to the first power)Solution© 2006 Paul Dawkins 60http://tutorial.math.lamar.edu/terms.aspx