Unit 7

Units 1 to 6 Review

Sinusoidal Functions and Graphs

The sine function can be plotted on a graph with the angle measure on the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math»-axis and the value of the sine ratio on the «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-axis.


The same is true for the cosine ratio.


The maximum «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-value in each graph is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»1«/mn»«/mstyle»«/math» because both ratios are based on the length of one of the legs of a right triangle divided by the hypotenuse. The hypotenuse is always the longest side of a right triangle, so the ratios will never be greater than «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»1«/mn»«/mstyle»«/math».

The period of both functions, or the angle measure that shows a full rotation, is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup»«mn»360«/mn»«mo accent=¨true¨»§#176;«/mo»«/msup»«/mstyle»«/math» or «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»2«/mn»«mo»§#960;«/mo»«/mrow»«/mstyle»«/math» radians.


The tangent has no minimum and no maximum. It regularly repeats itself every «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup»«mn»360«/mn»«mo accent=¨true¨»§#176;«/mo»«/msup»«/mstyle»«/math», or «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/mstyle»«/math» radians, and has regular vertical asymptotes.