Bellringer 3-28

• What is the area of a circular sector with radius = 9 cm and a central angle of θ = 45°?

Homework Section 5.2

• Pg. 251 (17, 21, 24, 28, 29)• 17. 20𝜋/3 (20.9 cm)• 21. 5𝜋/36 (.44 in)• 24. 35.8°• 28. 65.45 ft2• 29. 16.97 in2

Section 5.3 – Circular Functions

• Definition of Sine and Cosine

• If the terminal side of an angle θ in standard position intersects the unit circle at P(x,y), then cos θ = x and sin θ = y.

Sine and Cosine

• Ex. What is the sin 90°? (Draw circle and find coordinates.)

Sine and Cosine (2)

• What is the cos 𝜋?

Sine and Cosine (Functions of an Angle)

• For any angle in standard position with θ, a point P(x,y) on its terminal side, and r = , the sine and cosine functions of θ are as follows:

sin θ = cos θ =

Example 1

• Find the values of sine and cosine functions of an angle in standard position with measure θ if the point with coordinates (3,4) lies on its terminal side.

Example 2

• Find sin θ when cos θ = and the terminal side of θ is in the first quadrant.

6 Trigonometric Functions

• Sine, Cosine, Tangent, Cosecant, Secant, Cotangent

• sin θ = cos θ = tan θ =

• csc θ = sec θ = cot θ =

• Notice cosecant is the reciprocal of sine…• csc θ = 1/sin θ

Example

• The terminal side of an angle θ in standard position contains the point with coordinates (8, -15). Find the values of all 6 trig. Functions.

Chart for signs in Quadrants

Homework 5.3

• Pg. 260 (25, 28, 32)