Precalc/Trig Chapter 6: graphing/inverse trig, verifying identities, laws of sin+cos (copy)

5.0(1)
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/85

flashcard set

Earn XP

Description and Tags

for the class at IWA; includes info from previous chapter to make sure everyone knows it for our test

Pre-Calculus

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

86 Terms

1
New cards

general equations for sine and cosine graphs

f(x) = Asin(Bx-C)+D and Acos(Bx-C)+D

2
New cards

What does A mean in an equation?

Amplitude (how far the graph goes up, how far the graph goes down)

3
New cards

What does B mean in an equation?

Frequency (number of cycles in 2pi; when B=1 there is one cycle in 2pi)

4
New cards

What does D mean in an equation?

vertical shift

5
New cards

What is the phase (horizontal) shift in a sin/cos equation?

C/B

6
New cards

Period in a sin/cos graph

2pi/B

7
New cards

To graph a sin/cos graph…

divide the period by four, giving you the minimums, maximums, and intercepts

8
New cards

Range

y values

9
New cards

domain

x values

10
New cards

How do you find a period in a graph?

count length of one cycle (one up, one down)

11
New cards

How do you find B from a graph

set 2pi/B equal to the period and solve

12
New cards

If the B value in a tangent or cotangent graph is 1, the period is…

pi

13
New cards

to graph tangent or cotangent, fine the values where the function is —. These will be — — —.

undefined, vertical asymptote values

14
New cards

general equations for tan and cot graphs

y=tanx and y=cotx

15
New cards

What is the period in a tan/cot graph if B is NOT 1?

pi/B

16
New cards

For tangent, set Bx = —, —, — to find vertical asymptotes

-pi/2, pi/2, 3pi/2

17
New cards

For cotangent, set Bx = —, —, — to find vertical asymptotes

-pi, 0, pi

18
New cards

To graph a csc or sec graph…

use the reciprocal graph as a guide. The x intercepts will create vertical asymptotes on the reciprocal graphs

19
New cards

On csc and sec graphs, the x-ints from the guide graphs are…

vertical asymptotes

20
New cards

On csc and sec graphs, the relative max/mins from the guide graphs are…

vertexes

21
New cards

Range restrictions for inverse trig

sin and csc: q1 and q4

tan and cot: q1 and q4

cos and sec: q1 and q2

22
New cards

y=ArcSinx is the same as…

y=sin^-1x

23
New cards

each inverse trig expression has only — —-, which MUST be in the — restriction.

one answer, range

24
New cards

for special angle value expressions, evaluate the inside inverse trig function for the —, then find the — —.

angle, trig ratio

25
New cards

For trig values with numbers not on the unit circle, — — — from the inverse trig statement, then find the — —.

draw the triangle, trig ratio

26
New cards

when simplifying a trig function in terms of x, draw a triangle, fill in the missing side with a — — and find the trig ratio

x expression

27
New cards

reciprocal identity of sinx

1/cscx

28
New cards

reciprocal identity of cosx

1/secx

29
New cards

reciprocal identity of tanx

1/cotx

30
New cards

reciprocal identity of cscx

1/sinx

31
New cards

reciprocal identity of secx

1/cosx

32
New cards

reciprocal identity of cotx

1/tanx

33
New cards

sin²x + cos²x= —

1

34
New cards

1+tan²x= —

sec²x

35
New cards

1+cot²x= —

csc²x

36
New cards

1-sin²x and sin²x-1= —

cos²x

37
New cards

1-cos²x and cos²x-1= —

sin²x

38
New cards

even-odd identity rules

cos and sec will be pos with a negative x input (will still be positive if +x). Other ratios will be negative with a negative x.

39
New cards

sin(A+B)

sinAcosB+cosAsinB

40
New cards

sin(A-B)

sinAcosB-cosAsinB

41
New cards

cos(A+B)

cosAcosB-sinAsinB

42
New cards

cos(A-B)

cosAcosB+sinAsinB

43
New cards

(note: mrs. rich said this won’t be on the test, but it’s here for memorization.)

tan(A+B)

tanA+tanB/1-tanAtanB

44
New cards

(note: mrs. rich said this won’t be on the test, but it’s here for memorization.)

tan(A-B)

tanA-tanB/1+tanAtanB

45
New cards

know what functions are positive in what quadrants

q1: all

q2: sin csc

q3: tan cot

q4: cos sec

46
New cards

what would you do when given an equation like sin(pi/3 + pi/4)?

write out equation and use triangles to find values. then solve.

47
New cards

what would you do when given an equation like sin(5pi/12)?

find numbers that add or subtract to what is in parenthesis and also simplify to /4, /3, or /6. Then solve as if you were given the numbers.

48
New cards

If given some ratios of A and B in certain quadrants, draw — and then — as normal.

triangles, solve

49
New cards

sin2x

2sinxcosx

50
New cards

cos2x

cos²x-sin²x

51
New cards

(note: mrs. rich said this won’t be on the test, but it’s here for memorization.)

tan2x

2tanx/1-tan²x

52
New cards

In a question where you are given a trig ratio and its quadrant, you would…

draw the triangle and plug the subsequent values/ratios into what the question asks for

53
New cards

angles and measurements for 30/60/90 triangle

knowt flashcard image
54
New cards

angles and measurements for 45/45/90 triangle

knowt flashcard image
55
New cards

sin in terms of x,y

y

56
New cards

cos in terms of x,y

x

57
New cards

tan in terms of x,y

y/x

58
New cards

csc in terms of x,y

1/y

59
New cards

sec in terms of x,y

1/x

60
New cards

cot in terms of x,y

x/y

61
New cards

unit circle points and angles

knowt flashcard image
62
New cards

tangent graph

knowt flashcard image
63
New cards

cotangent graph

knowt flashcard image
64
New cards

sin graph

knowt flashcard image
65
New cards

csc graph

knowt flashcard image
66
New cards

cos graph

knowt flashcard image
67
New cards

sec graph

knowt flashcard image
68
New cards

oblique triangle

triangle that does not contain a right angle

has either three acute angles or two acute angles and one obtuse angle

69
New cards

To use the law of sines…

need two angles and the side across from one of the angles OR two sides and the angle across from one of the sides

70
New cards

Only — ratios are used to solve for one unknown part of the triangle when using the law of sines.

two

71
New cards

ambiguous case

it’s possible to have 0, 1, or 2 triangles for two sides and one angle

72
New cards

In the ambiguous case, you have 0 triangles when…

sin > 1

73
New cards

In the ambiguous case, you have 1 triangle when…

adding up the given angle and ang equal to one you solved for is > 180

74
New cards

In the ambiguous case, you have 2 triangles when…

adding up given angle and ang equal to one you solved for is < 180

75
New cards

Area for oblique triangle

½ bc SinA, ½ ab SinC, ½ ac SinB

76
New cards

law of cos is needed to solve for the missing part for:

SAS, SSS

77
New cards

once missing part of oblique triangle is found with law of cos, — — — can be used

law of sines

78
New cards

cos of pi/6

square root of 3/2

79
New cards

sin of pi/6

1/2

80
New cards

tan of pi/6

square root of 3/3

81
New cards

sin of pi/4

square root of 2/2

82
New cards

cos of pi/4

square root of 2/2

83
New cards

tan of pi/4

1

84
New cards

cos of pi/3

1/2

85
New cards

sin of pi/3

square root of 3/2

86
New cards

tan of pi/3

square root of 3