1. Chapters 13 – 14
Trigonometry

2. What are Radians?
• Angles can be measured in either degrees
or radians.
• One radian is equal to the measure of a
central angle in a circle whose arc length
equals 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, and
vertex 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 of
an angle θ in standard position. Evaluate the
6 trig functions of θ.

16. Example
• Let (-5, 12) be a point on the terminal side
of θ. Evaluate the 6 trig functions.

17. Your Turn!
• Let (-4, -3) be a point on the terminal side of
θ. Evaluate the 6 trig functions of θ.

18. Modeling with Trig
• A circular clock gear is 2 inches wide. If the
tooth at the farthest right edge starts 10
inches above the base of the clock, how far
above the base is the tooth after it rotates
240 counterclockwise?

19. Graphing Sine Functions
θ sin θ
0
π/4
π/2
3π/4
π

20. Graphing Cosine Functions
θ cos θ
0
π/4
π/2
3π/4
π

21. Vocab:
• Cycle – shortest repeating portion.
• Period – horizontal length of each cycle.
• Amplitude – height of the graph, measured
from the center.

22. Graphing Tangent Functions
θ tan θ
-π
-3π/4
-π/2
-π/4
0
π/4
π/2
3π/4
π

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 double
its amplitude.
• the horizontal stretch of y = cos x that will
double 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 original
amplitude.