Ch 4 Trig Functions

4.1 Radian and Degree Measures Converting from Radians to Degrees Converting from Degrees to Radians

4.1 Angles in Standard Position vertex at origin initial side on positive x-axis terminal side counter-clockwise from initial side

4.1 Arc Length

Find the length of the arc intercepted by a central angle of 45 o in a circle with a radius of 10cm.

4.1 Linear and Angular Speed

4.1 degrees, minutes, seconds Converting minutes and seconds to degrees. Converting decimal degrees to minutes and seconds.

4.2 Unit Circle

4.4 All Students Take Calculus

4.4 Evaluating Trig Functions of Any Angle Given and, find and. tan (-) and cos (+) = QIV Draw angle from origin to x-axis. -5 4

4.4 Reference Angle Angle to x-axis.

4.5 Graphs of Sine and Cosine Functions

Find the amplitude and period.

4.5 Graphs of Sine and Cosine Functions Vertical and Horizontal Shifts

4.7 Inverse Trig Functions Take the sin of an angle to get a ratio Take the arcsin of a ratio to get an angle

4.7 Inverse Trig Functions Find the exact value

5.1 Identities Pythagorean Identities Quotient Identities Be familiar with identities on the inside of front and back cover of book (on blue cheat sheet).

6.1 Law of Sines The ratios of angles and corresponding sides are equal. Find b.

6.2 Law of Cosines Find b.

6.3 Vectors

Vectors A vector whose initial point is at the origin is in standard position. The magnitude of a vector is its length.

Vectors The magnitude (length) of v

Vectors The components (direction) of v one unit to the left two units up

Scalar Multiplication of Vectors Vectors can be multiplied to change its scale.

Vectors Addition Vectors can be added. = commutative

Addition of Vectors

The Unit Vector To get a unit vector, divide the vector by its magnitude. u = unit vector

i and j horizontal and vertical components horizontal component i vertical components j v = v = i j

The Unit Vector Write a vector as a combination of unit vectors. i represents a horizontal unit vector j represents a vertical unit vector i ii j j j j

Unit Vectors on Unit Circle u Find the magnitude and direction angle of the vector.