Your Turn!• Evaluate without a calculator:1. cos (-150 )2.
Vocab:• Angles are made of two rays:▫ The initial side is fixed▫ The terminal side is rotated about the vertex.• An angle whose initial side is the + x-axis, andvertex is the origin is in Standard Position.
General Definition of Trig Functions• If θ is an angle in standard position,and (x, y) is a point on the terminal side:
Evaluating Trig Functions• Let (3, -4) be a point on the terminal side ofan angle θ in standard position. Evaluate the6 trig functions of θ.
Example• Let (-5, 12) be a point on the terminal sideof θ. Evaluate the 6 trig functions.
Your Turn!• Let (-4, -3) be a point on the terminal side ofθ. Evaluate the 6 trig functions of θ.
Modeling with Trig• A circular clock gear is 2 inches wide. If thetooth at the farthest right edge starts 10inches above the base of the clock, how farabove the base is the tooth after it rotates240 counterclockwise?
Vocab:• Cycle – shortest repeating portion.• Period – horizontal length of each cycle.• Amplitude – height of the graph, measuredfrom the center.
Graphing Tangent Functionsθ tan θ-π-3π/4-π/2-π/40π/4π/23π/4π
Analyzing Trig Graphs• Identify the amplitude and period of each:y = 2 sin x y = 1/2 cos x
Writing Trig Functions• Write an equation for:• the translation 3 units up of y = sin x.• the translation π units right of y = cos x.• the vertical stretch of y = sin x that will doubleits amplitude.• the horizontal stretch of y = cos x that willdouble the period.
Your Turn!• Write an equation of y = sin x after being:• shifted 3 units down• shifted π/2 units left• and vertically compressed to half the originalamplitude.