Chapter 5

Question 1

Strategies for simplifying using trig identities?

Answer 1

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

Question 2

What are the trig identities

Answer 2

sin^2 + cos^2 = 1
1 + tan ^2 = sec^2
1 + cot^2 = csc^2

Question 3

Difference of squares-

sec^2 x - 1 creates what when factored

Answer 3

two binomials that are conjugates

Question 4

Verify Rules

Answer 4

Don’t touch the right side, transform left into the right

Question 5

what do you do with a quadratic trinomial?

2 sin^2x -sin x -1 =0

Answer 5

Lopezian method

Question 6

Solving simple trig equations steps

Answer 6

1) If there are common factors collect all trig functions on one side then factor or combine
2) if there are no common factors, use the appropriate ID to convert to a single trig function.

Question 7

sinku and cosku what do you do? 2sin3t-1=0

Answer 7

you let theta = 3t, or the k

Question 8

Find the EXACT VALUE. cos 75 degrees

Answer 8

Use sum and difference formulas. for example: cos(30+45) then use that formula cos (u + v)
both angles must be on unit circle!

Question 9

Solve a MULTIPLE ANGLE EQUATION

for example: 2cosx + sin2x

Answer 9

sin2u formula, plug it in, factor and solve. Tells you what quadrant you can find it in as well

Question 10

Half Angle Formulas? for example: find the exact value of sin 105 degrees

Answer 10

105 is half of 210, use sin half angle formula using the new number.