3 5 Equivalent Trigonometric Expressions Mrs Lisa Allen

(3 -5) Equivalent Trigonometric Expressions Mrs. Lisa Allen Honors Pre-calculus Saucon Valley High School

Example 1 Write the expression in terms of sines or cosines only

Example 2 Convert the first expression to the second expression (sec +1)(sec - 1) ; Using Foil (sec Method Relate tangent squared & secant squared by an identity! +1)(sec - 1)

FACTORING THE DIFFERENCE OF 2 SQUARES Factor the following expressions

Example 3 Convert the first expression ; to the second expression. Factor the numerator and denominator Cancel Common Factors QED

FACTORING REVIEW THE DIFFERENCE/SUM OF 2 CUBES The DIFFERENCE OF 2 CUBES The SUM OF 2 CUBES

FACTORING REVIEW FACTOR using the formulas. 1) √ 2) √

Example 4 Convert the first expression ; to the second expression √ Write 8 as a perfect cube, 4 as a perfect square √ The numerator factors as the sum of two cubes √ The denominator factors as the sum of two squares √ Cancel common factors √ And Simplify

Example 5 Write the expression in terms of sin. Multiply each fraction by the missing factor of the LCD = sin (1+cos ) and combine fractions Use the identity cos^2 + sin^2 = 1 Simplify Factor the Numerator and simplify √

Example 6 Write the expression in terms of cos. Change tan to sin/cos. 1 = cos^2/cos^2 Combine fractions Use Pythagorean Id. Simplify and Multiply the two fractions √

Example 7 Convert to √

Homework P. 137 Practice Exercises # 5, 10, 15, 20, 22, 25, 26, 30, 33 o