Home Trig Functions of Real Numbers Compound Angles (a +/- b) Sum/Product Formulas Double Angle Formulas Trig. Equations Inverse Trig. Functions Summary&Test

UNIT 8  :  TRIGONOMETRIC FUNCTIONS

LESSON 7:  SUMMARY & TEST

LESSON 1:  TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS HOMEWORK QUESTIONS

Angles in Standard Position using the Unit Circle:

Special Angles Table

 1

LESSON 2 :  COMPOUND ANGLE FORMULAS

In this section we develop the compound angle formulas, which allow us to write the sine or cosine of (x + y) or (x – y) in terms of the sines and cosines

of the individual angles x and y.  See your text for proofs of the following formulas.

LESSON 3:  SUM TO PRODUCT AND PRODUCT TO SUM FORMULAS

LESSON 4:  DOUBLE ANGLE FORMULAS

LESSON 5:  SOLVING TRIGONOMETRIC EQUATIONS

LESSON 6:  INVERSE TRIGONOMETRIC FUNCTIONS

Summary:  The graphs of the inverse trigonometric functions are reviewed below.

 Inverse Function Domain Range Example y = sin-1x y = cos-1x y = tan-1x

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 ].

The Unit Circle for Special Angles