Trigonometry Review

Angle Measurement To convert from degrees to radians, multiply byTo convert from radians to degrees, multiply by radians, so radians

Special Angles r=1

Special Angles - Unit Circle Coordinates r=1 π/3 5π/6 π/4 π/2 2π/3 3π/4 π/6 π0 3π/2

Trig Functions - Definitions (x,y) r 

Trig Functions - Definitions  opp adj hyp

Trig Functions - Definitions

Trig Functions Signs by quadrants all functions positivesin, csc positive tan, cot positivecos, sec positive

Special Angles - Triangles example:

Special Angles - Triangles

Special Angles - Unit Circle r=1

Special Angles For the angles example: Use the unit circle points (1,0), (0,1), (-1,0) and (0,-1) or look at the graphs for the trig functions r = 1 (1,0) (0,1) (0,-1) (-1,0)

Graphing Trigonometry Functions Basic Graphs y = sin x 1 -π/2π/2π3π/22π2π Period is and amplitude is 1.

Graphing Trigonometry Functions Basic Graphs -π/2π/2π3π/22π2π y = cos x 1 Period is and amplitude is 1.

Special Angles and Graphs Using the graph for

Graphing Trig Functions Amplitude Change y= a sin x stretches or compresses the graph vertically y = a sin x a -a -π/2π/2π3π/22π2π Period is and amplitude is a.

Graphing Trig Functions Phase Shift y = sin(x - b) slides graph right by b units b 1 2π+b y = sin(x - b) Period is and amplitude is 1.

Graphing Trig Functions Phase Shift y = sin(x + b) slides graph left by b units 1 -b2π - b y = sin(x + b) Period is and amplitude is 1.

Graphing Trig Functions Period Change y = sin cx stretches or compresses the graph horizontally 1 2π/c Period is and amplitude is 1.

Trig Identities ReciprocalQuotient

Trig Identities Pythagorean

Trig Identities Double Angle

Trig Identities Sum and difference

Inverse Trig Functions is equivalent to

Solving Trig Equations Use algebra, then inverse trig functions or knowledge of special angles to solve. example: if in quadrants I and II and since