5.5

Question 1

45 degrees

Answer 1

pi/4

Question 2

square root method

Answer 2

isolate x^2
√ both sides

Question 3

square rooting use

Answer 3

+/-

Question 4

solving quadratics by factoring

Answer 4

get =0
factor
set each =0
solve

Question 5

trig identities work for

Answer 5

any value of x that is in the domain of the functions involved

Question 6

every x value where the line y=1/2 intersects with the function y=sinx

Answer 6

is a solution to the equation sinx=1/2

Question 7

another way of looking at it

Answer 7

pi/6 and 5pi/6 are solutions as well as every coterminal angle with pi/6 and 5pi/6

Question 8

if a specific interval is given for solutions

Answer 8

you do not need to add the infinite number of periods

Question 9

period of tangent

Answer 9

pi so pin

Question 10

period of sin/cos

Answer 10

2pin

Question 11

use both options with 2pin except for

Answer 11

tangent

Question 12

multiple angle identities

Answer 12

use the horizontal shrink to find solutions

Question 13

from [0, 2pi) there are

Answer 13

four solutions, two in each period so shrink the original solutions ands add the new period

Question 14

solving equations with a calculator

Answer 14

use the inverse function to find the reference (first quadrant) angle, then apply that to the proper quadrants

Question 15

you can check multiple angle identities by

Answer 15

substituting them into the original equation

Question 16

in csc or sec

Answer 16

turn into recipricols

Question 17

applying horizontal shrink

Answer 17

divide out coefficient on all erms and add pin number together

Question 18

from Q1 to Q2

Answer 18

do pi - value given by calculator

Question 19

cos memorize

Answer 19

43210
0, 30, 45, 60, 90
root and divide by 2
always use lcf

Question 20

sin memorize

Answer 20

01234
0, 30, 45, 60, 90
root and divide by 2
always use lcf

Question 21

tan memorize

Answer 21

0, 30, 45, 60, 90
0, always use √3/3, 1, √3, und.

Question 22

quotient identities

Answer 22

tan and cot

Question 23

quotient tan

Answer 23

sin/cos

Question 24

quotient cot

Answer 24

cos/sin

Question 25

recipricol identities

Answer 25

1 over

Question 26

recipricol sin

Answer 26

1/csc

Question 27

recipricol cos

Answer 27

1/sec

Question 28

recipricol tan

Answer 28

1/cot

Question 29

recipricol csc

Answer 29

1/sin

Question 30

recipricol sec

Answer 30

1/cos

Question 31

recipricol cot

Answer 31

1/tan

Question 32

pythagorean identities

Answer 32

squared equals one

Question 33

pythagorean sin

Answer 33

sin^2+cos^2=1

Question 34

pythagorean sec

Answer 34

sec^2-tan^2=1

Question 35

pythagorean csc

Answer 35

csc^2-cot^2=1

Question 36

even odd identities

Answer 36

cos and sec are only positive

Question 37

cofunction identities

Answer 37

pi/2 - thta

Question 38

sin cofunction

Answer 38

cos

Question 39

cos cofunction

Answer 39

sin

Question 40

tan cofunction

Answer 40

cot

Question 41

cot cofunction

Answer 41

tan

Question 42

csc cofunction

Answer 42

sec

Question 43

sec cofunction

Answer 43

csc

Question 44

“Function period vs solution spacing”

Answer 44

Because the equation’s solutions repeat every π or 2 𝜋 2π, even though both functions have period 2 𝜋 2π.

Question 45

Why is factoring important in trig?

Answer 45

Every factor could give valid solutions. Missing one = missing part of the solution set.

Question 46

Front: Why do we sometimes need two general solutions for sin x = value?

Answer 46

Count the number of times the value occurs in [0, 2π). Each distinct solution gets its own “+2π n” in the general solution.

Question 47

How do you find tangent solutions in [-π, π)?

Answer 47

Find reference angle. Determine which quadrants tangent is negative/positive. Convert angles > π to negative by subtracting 2π until inside [-π, π).

Question 48

if answer never happens

Answer 48

no solution

Question 49

Front: How do you convert sine negative angles to [-π, π)?

Answer 49

Use reference angle and put in Quadrants III (negative) & IV (negative).