Chapter 5

Question 1

Name the strategies used to SIMPLIFY using fundamental identities.

Answer 1

1) Look for a common factor
2) Recognize the Pythagorean identities
3) Rewrite everything in terms of sin and cos
4) When needed, find a common denominator

Question 2

Name the Pythagorean Identities

Answer 2

sin²x + cos²x = 1
1 + tan²x = sec²x
1 + cot²x = csc²x

Question 3

Factor each expression.

Answer 3

Factor the same way you factor anything

Question 4

Product property of logarithms

Answer 4

ln(u*v)= ln u + ln v

Question 5

Quotient Property of logarithms

Answer 5

ln (u/v) = ln u - ln v

Question 6

Rewrite the expression so that it is NOT in fractional form

Answer 6

multiply the bottom part of the fraction by the CONJUGATE

Question 7

Conjugate

Answer 7

same first two terms of an expression separated by different sign

Question 8

Strategies for VERIFYING trig identities

Answer 8

1. Do NO touch the right hand side

2. Transform left side to turn it into right side

Question 9

SOLVING simple trigonometric equations strategies

Answer 9

Collect like terms, make sure all trig functions are on one side of the equation, use unit circle to find out answers (CAST)

Question 10

2 or more functions in the same equation?

Answer 10

All functions in the same side, use lopezian method or use zero product property

Question 11

Checking Answers?

Answer 11

Insert the x value into the equation, make sure the squared sign is outside the brackets. leave the other value like the one by itself.