Ch 4 Trig Functions 4 1 Radian and

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 terminal side counter-clockwise from initial side vertex at origin initial side on positive x-axis

4. 1 Arc Length

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 10 cm.

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 tan (-) and cos (+) = QIV Draw angle from origin to x-axis. and 4 . -5

4. 4 Reference Angle to x-axis.

4. 5 Graphs of Sine and Cosine Functions

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. 4 5 -3

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 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 j j i i i

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