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

Algebra/Trig ReviewFrom this unit circle we can see that⎛2π⎞ 3sin ⎜ ⎟ = and⎝ 3 ⎠ 2⎛ 2π⎞ 3sin ⎜− ⎟=−.⎝ 3 ⎠ 2This leads to a nice fact about the sine function. The sine function is called an oddfunction and so for ANY angle we havesin − θ =− sin θ( ) ( )11.⎛7π⎞cos⎜⎟⎝ 6 ⎠ and ⎛ 7π⎞cos⎜−⎟⎝ 6 ⎠SolutionFor this example notice that 7 π ππ= π + so this means we would rotate down6 667ππfrom the negative x-axis to get to this angle. Also − =−π− so this means we6 6would rotate up 6π from the negative x-axis to get to this angle. These are bothshown on the following unit circle along with appropriate coordinates for theintersection points.© 2006 Paul Dawkins 49http://tutorial.math.lamar.edu/terms.aspx