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- 1. Chapters 13 – 14Trigonometry
- 2. What are Radians?• Angles can be measured in either degreesor radians.• One radian is equal to the measure of acentral angle in a circle whose arc lengthequals the radius.Unit circle
- 3. Review of Unit Conversions• To convert between units of measure:• Set up a proportion and solve.• Example: 42 feet is how many yards?
- 4. Converting Degrees & Radians• Fill in the given and cross multiply to solve.• Example:• Convert 110 to radians
- 5. Examples:• Convert to degrees.• Convert to degrees.
- 6. Your Turn!• Convert -220 to radians.• Convert to degrees.
- 7. Special Right Triangles Review• 45 – 45 – 90• 30 – 60 – 90
- 8. Six Trig Functions• sin θ = =• cos θ = =• tan θ = =• csc θ = =• sec θ = =• cot θ = =“cosecant”“secant”“cotangent”
- 9. Evaluating Trig Functions• Without a calculator!!1. Find the angle on the unit circle.2. Evaluate using cosine, sine, or both.3. Leave answers in reduced radical form.NO DECIMALS!
- 10. Examples•• tan 240•
- 11. • csc (-225 )••
- 12. Your Turn!• Evaluate without a calculator:1. cos (-150 )2.
- 13. 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.
- 14. General Definition of Trig Functions• If θ is an angle in standard position,and (x, y) is a point on the terminal side:
- 15. 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.
- 16. Example• Let (-5, 12) be a point on the terminal sideof θ. Evaluate the 6 trig functions.
- 17. Your Turn!• Let (-4, -3) be a point on the terminal side ofθ. Evaluate the 6 trig functions of θ.
- 18. 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?
- 19. Graphing Sine Functionsθ sin θ0π/4π/23π/4π
- 20. Graphing Cosine Functionsθ cos θ0π/4π/23π/4π
- 21. Vocab:• Cycle – shortest repeating portion.• Period – horizontal length of each cycle.• Amplitude – height of the graph, measuredfrom the center.
- 22. Graphing Tangent Functionsθ tan θ-π-3π/4-π/2-π/40π/4π/23π/4π
- 23. Analyzing Trig Graphs• Identify the amplitude and period of each:y = 2 sin x y = 1/2 cos x
- 24. 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.
- 25. 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.

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