Objectives of this Section

1 / 25

# Objectives of this Section - PowerPoint PPT Presentation

Sullivan Algebra and Trigonometry: Section 6.5 Unit Circle Approach; Properties of the Trig Functions. Objectives of this Section Find the Exact Value of the Trigonometric Functions Using the Unit Circle Determine the Domain and Range of the Trigonometric Functions

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Objectives of this Section' - lilah-horton

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Sullivan Algebra and Trigonometry: Section 6.5Unit Circle Approach; Properties of the Trig Functions
• Objectives of this Section
• Find the Exact Value of the Trigonometric Functions Using the Unit Circle
• Determine the Domain and Range of the Trigonometric Functions
• Determine the Period of the Trigonometric Functions
• Use Even-Odd Properties to Find the Exact Value of the Trigonometric Functions

The unit circle is a circle whose radius is 1 and whose center is at the origin.

Since r = 1:

becomes

y

(0, 1)

x

(-1, 0)

(1, 0)

(0, -1)

y

(0, 1)

P = (a, b)

x

(-1, 0)

(1, 0)

(0, -1)

Let t be a real number and let P = (a, b) be the point on the unit circle that corresponds to t.

The sine function associates with t the y-coordinate of P and is denoted by

The cosine function associates with t the x-coordinate of P and is denoted by

y

(0, 1)

P = (a, b)

x

(-1, 0)

(1, 0)

(0, -1)

y

a

x

b

r

P=(a,b)

(5, 0)

y

(0, 1)

P = (a, b)

x

(-1, 0)

(1, 0)

(0, -1)

The domain of the cosine function is the set of all real numbers.

The domain of the tangent function is the set of all real numbers except odd multiples of

The domain of the secant function is the set of all real numbers except odd multiples of

The domain of the cotangent function is the set of all real numbers except integral multiples of

The domain of the cosecant function is the set of all real numbers except integral multiples of

Range of the Trigonometric Functions

Let P = (a, b) be the point on the unit circle that corresponds to the angle . Then, -1 <a < 1 and -1 <b< 1.