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Trig Functions of Real Numbers

Compound Angles (a +/- b)

Sum/Product Formulas

Double Angle Formulas

Trig. Equations

Inverse Trig. Functions

Summary&Test

jdsmathnotes

 


 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

 

 

 

 

 

 

 

 

 

Text Box: Opposite Angle Identities
 

 

 

 

 

 

 

 

 


 

 

Text Box: Periodic  Identities
 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 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.

 

 

Text Box: Addition Formulas for Sine and Cosine

 


 

 

Text Box: Co-related Angle Formulas

Text Box: Related Angle Formulas

 

 

 

 

 


 

 

 LESSON 3: SUM TO PRODUCT AND PRODUCT TO SUM FORMULAS

 

 

Text Box: Product-to-Sum Formulas

 


 

Text Box: Sum-to-Product Formulas

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LESSON 4: DOUBLE ANGLE FORMULAS

 

 

Text Box: Alternate Double-Angle Formulas

Text Box: Double-Angle Formulas

 

Text Box: Half-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

 

 

 

 

 

 

 

Text Box:

 

 


 

 

Text Box:

 


 

 

 

 

 

 

 

 

 

 

 

 

 

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

 

 

 

 

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