Chapter 10 - NCPN

More documents

Recommendations

Info

$hvvrq 6\vwhpv ri &rqlf 6hfwlrqv - NCPN$

Lesson 10.2 Evaluating Trigonometric Functions Objectives Convert between degrees and radians. Find the length of an arc. Evaluate trigonometric functions. Radians and Degrees To draw an angle in standard position, place the vertex at the origin and one ray of the angle along the positive x-axis. The ray on the x‐axis is the initial side of the angle, and the other ray is the terminal side of the angle. To measure an angle in standard position, find the amount of rotation counterclockwise from the initial side to the terminal side. Angles can be measured in degrees and in radians. A complete rotation is 360° or 2π radians. Example 1 Converting Radians and Degrees Find the radian measure of an angle with a measure of 120°. Solution A full rotation of 360° is equal to 2π radians. Set up and solve a proportion for the angle measure in radians. 120° = r radians 360° 2 π radians 120 • 2π = 360° • r 240π = r 360 2π = r 3 An angle with a measure of 120° has a measure of 2 3≠ , or approximately 2.1 radians. 442 Chapter 10 Trigonometric Functions and Identities
Arc Length The unit circle has a radius of 1 unit and is centered about the origin. A central angle of a circle is an angle with a vertex at the center of the circle. An intercepted arc is the part of the circle that has endpoints on the sides of the central angle and all points in the interior of the angle. Arc Length If a circle with radius r has a central angle of measure θ radians, the length, l, of the intercepted arc is l = rθ. Example 2 Measuring Arc Length Find the length of the intercepted arc in the circle. Solution The measure of the central angle is 1.9 radians, and the circle has a radius of 6 centimeters. Use the formula for the length of an intercepted arc. l = rθ l = (6)(1.9) l = 11.4 The length of the intercepted arc is 11.4 centimeters. 10.2 Evaluating Trigonometric Functions 443
Page 1 and 2: Chapter 10 Contents 10.1 Right Tria
Page 3 and 4: Lesson 10.1 Right Triangle Trigonom
Page 5 and 6: Solution Use the definitions of the
Page 7 and 8: Solve for x in each right triangle.
Page 9: 30. A wheelchair ramp is 20 feet lo
Page 13 and 14: Using a Calculator A scientific cal
Page 15 and 16: Find the length of the intercepted
Page 17 and 18: Lesson 10.3 Inverse Trigonometric F
Page 19 and 20: see margin After taking off, a comm
Page 21 and 22: 20. What is the angle of descent of
Page 23 and 24: The y-values on the unit circle are
Page 25 and 26: Example 2 Graphing Cosine Functions
Page 27 and 28: Activity Using a Graphing Calculato
Page 29 and 30: 25. The function y = 3sin ≠ t mod
Page 31 and 32: Ongoing Assessment In PQR, m∠P =
Page 33 and 34: Activity Ambiguous Cases Two triang
Page 35 and 36: Lesson Assessment Think and Discuss
Page 37 and 38: 23. Two points in a forest, A and B
Page 39 and 40: Lesson 10.6 Verifying Trigonometric
Page 41 and 42: Activity 2 Using the Pythagorean Id
Page 43 and 44: Lesson 10.7 Angle Sum and Differenc
Page 45 and 46: Practice and Problem Solving Use a
Page 47 and 48: Lesson 13.4 Double-Angle and Half-A
Page 49 and 50: When Trigonometric Function Values
Page 51 and 52: Practice and Problem Solving Use a
Page 53 and 54: Lesson 10.9 Solving Trigonometric E
Page 55 and 56: Use the Zero-Product Property to se
Page 57 and 58: Practice and Problem Solving Solve
Page 59 and 60: Math Labs Activity 1: The Circle of
Page 61 and 62:
Activity 3: The Sine Curve of Biorh
Page 63 and 64:
3 Hold a protractor upside down so
Page 65 and 66:
3 Cale, Tammie, and Allison are mem
Page 67 and 68:
8 Bella does freelance marketing wo
Page 69 and 70:
Health Occupations 13 Dmitri wants
Page 71 and 72:
Lessons 10.5 and 10.6 Review Exampl
Page 73:
Standardized Test Practice Multiple
show all

Chapter 10 - NCPN

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?