Home Radians & Degrees Trig. Definitions using {x, y, r} Trig. Definitions using Unit Circle Trig. Functions & Graphs Transformations Trig. Identities Trig. Eauations Summary&Test

UNIT 7  :  TRIGONOMETRIC FUNCTIONS

LESSON 8 :  TRIGONOMETRIC FUNCTIONS REVIEW

Example 1: Conversions from radian measure to degree measure

Solution:

Example 2: Conversions from degree measure to radian measure

Solution:

Angles in Standard Position using  {x, y, r}:

Definition:   An angle is in standard position if it has its vertex at the origin and  initial arm along the positive x-axis.  The terminal arm is found by rotating

the initial arm about the origin to a terminal position in one of the 4 quadrants.  The rotation is positive if it is in the counter – clockwise direction and negative

if in the clockwise direction.

Angles in Standard Position using the Unit Circle:

Definition: Coterminal angles have the same initial arm and same terminal arm.  They can be found by adding or subtracting 3600 from the given angle.

Summary:

Special Angles Table:

 1

The Unit Circle for Special Angles

Example :

Trigonometric Functions of Real Numbers Using the CAST RULE & Special Angles Table :

The CAST rule:

The CAST RULE is a memory aid which tells us the sign of the trig ratios in the various quadrants.

In the first quadrant ALL are positive.  This is denoted using the letter A.

In the second quadrant, SINE  is positive.  This is denoted by the letter S.

[ the other two ratios are negative ]

In the third quadrant, TANGENT  is positive.  This is denoted by the letter T.

[ the other two ratios are negative ]

In the fourth quadrant, COSINE  is positive.  This is denoted by the letter C.

[ the other two ratios are negative ].

Special Angles Table:

 1

Special Angles Table:

 1

Graphs of Trig. Functions

**See lesson 3 for the reciprocal graphs

Combinations of Transformations :   y = a sin k(xd) + c   and   y = a cos k(xd) + c

 x0 0 90 180 270 360 y 0 1 0 -1 0

Solving Trig. Equations:

Example:

Solution:

Basic Trigonometric Identities :

Example :

Proof: