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Math Unit 5 Test Flashcards

1
Q

Hypotenuse:

A

The longest side, always across from the Right Angle

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2
Q

Opposite:

A

Across from the INDICATED/GIVEN angle

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3
Q

Adjacent:

A

Helps form the INDICATED/GIVEN angle

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4
Q

SOH CAH TOH

A

Sin 0 = Opp/Hyp
Cos 0 = Adj/Hyp
Tan 0 = Opp/adj

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5
Q

There are 3 “Secondary Trig Ratios” They are…

A

the Reciprocals of the “Primary Trig Ratios”

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6
Q

Cosecant

A

Csc 0 = Hyp/Opp

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7
Q

Secant

A

Sec 0 = Hyp/Adj

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8
Q

Cotangent

A

Cot 0 = Adj/Opp

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9
Q

Angles 30°, 45° and 60° often occur in trigonometry

A

they are called SPECIAL angles
the triangles in which they are found are called SPECIAL TRIANGLES

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10
Q

What does ET look like?

A

Equilateral triangle split in half
Degrees - 90 and 60 at the bottom together, and 30 at the top
Sides - √3 (adj or opp), 2 (hyp), 1 (adj or opp)

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11
Q

What does IRT look like?

A

Triangle split in half
Degrees - 45, 45, 90
Sides - 1 (adj or opp), 1 (adj or opp), √2

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12
Q

When the angle is 30 what is cos?

A

√3/2

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13
Q

When the angle is 30 what is sin?

A

½

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14
Q

When the angle is 30 what is tan?

A

1/√3

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15
Q

When the angle is 45 what is cos?

A

1/√2

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16
Q

When the angle is 45 what is sin?

A

1/√2

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17
Q

When the angle is 45 what is tan?

A

1

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18
Q

When the angle is 60 what is cos?

A

½

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19
Q

When the angle is 60 what is sin?

A

√3/2

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20
Q

When the angle is 60 what is tan?

A

√3/1

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21
Q

From the UNIT CIRCLE diagram, we can see a rule in when RATIOS ARE POSITIVE in each of the 4 quadrants

A

This is often called the CAST RULE

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22
Q

C in

A

bottom right

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23
Q

A in

A

top right

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24
Q

S in

A

top left

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25
Q

T in

A

bottom left

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26
Q

A is

A

I

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27
Q

S is

A

II

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28
Q

T is

A

III

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29
Q

C is

A

IV

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30
Q

A range

A

0 - 90

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31
Q

S range

A

90 - 180

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32
Q

T range

A

180 - 270

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33
Q

C range

A

270 - 360

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34
Q

Cosine is positive in

A

C

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35
Q

All ratios are positive in

A

A

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36
Q

Sine is positive in

A

S

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37
Q

Tangent is positive in

A

T

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38
Q

To Find the exact value of the following (use a well-labelled diagram)

A

Drop the perpendicular to the x-axis after drawing the angle
Subtract the max angle from each quadrant to find the value

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39
Q

For 30 just

A

draw IRT otherwise it confuses you lol

40
Q

To Using the appropriate triangle, determine θ, if 0°≤ θ ≤ 360°

A

Figure out what special angle it is
What quadrants it is positive or negative dependingt on the trig ratio
Draw both angles in both quadrants and figure out the other angle by subtracting the og angle

41
Q

To Find the exact value of the following. Rationalize the denominator where necessary

A

Use the diagram for each one
Add/Multiple together using radical rules

42
Q

Angles

A

= Upper Case letters

43
Q

Side Length

A

= Lower Case letters

44
Q

Steps to Finding Side Lengths with Primary:

A
  1. Step 1: Label the sides (Hypotenuse, Opposite and Adjacent) of your triangle relative to the given angle
  2. Step 2: Determine which trig ratio to use (Sin, Cos or Tan?) by checking SOH CAH TOA
  3. Step 3: SET UP the equation with the unknown side and solve for the side length
45
Q

Steps to Finding Angles with Primary:

A
  1. Step 1: Label the sides (Hypotenuse, Opposite and Adjacent) of your triangle relative to the Angle you want to find
  2. Step 2: Determine which trig ratio to use (Sin, Cos or Tan?) by checking SOH CAH TOA
    Step 3: SET UP the equation with the unknown side and solve for the angles using the inverse trig ratios
46
Q

Elevation:

A

The angle is made between the HORIZONTAL and the line of sight UPWARDS to an object

47
Q

Depression:

A

The angle is made between the HORIZONTAL and the line of sight DOWNWARDS to an object

48
Q

Matching pair:

A

When you know the value of an ANGLE and its opposite SIDE

49
Q

Sine law is for…

A

NON-RIGHT Triangles with a MATCHING PAIR

50
Q

Sine law to find unknown SIDES…

A

a/Sine A = b/Sine B = c/Sine C

51
Q

Sine law to find unknown ANGLES…

A

Sine A/a = Sine B/a = Sine C/c

52
Q

Contained Angle:

A

When you know the value of an ANGLE and the TWO SIDES that create the angle

53
Q

Cosine law is for…

A

NON-RIGHT Triangles with TWO SIDES and a CONTAINED angle

54
Q

Cosine law to fine unknown SIDES…

A

c2 = a2 + b2 − 2ab cos(C)

55
Q

You can change cosine law (sides) just always make sure that

A

the side you are finding has it’s matching angle at the end of the formula

56
Q

Cosine law to find angles is when you have…

A

NON-RIGHT Triangles with ALL THREE SIDES

57
Q

Cosine law to find unknown ANGLES…

A

cosC = a^2 + b^2 - c^2/2ab

58
Q

You can change cosine law (angles) just swap

A

the matching side being subtracted for the matching angle being found

59
Q

To SOLVE a triangle means to find:

A

All unknown SIDES
All unknown ANGLES

60
Q

To find an area…

A
  1. Use cosine to find the contained angle
  2. Use SOHCAHTOA to find the height
  3. Use a=bh/2 to find the area
61
Q

To find boats/distance…

A
  1. Find the angle in the triangle by subtracting the barrings
  2. Convert the units by multiplying the km/hr by the hours to find the km
  3. Use cosine law to find x
62
Q

3-D Applications

A
  1. Draw it
  2. Find the missing angles using 180 - angle = or barrings subtract
  3. Use SOH CAH TOA to find missing sides
  4. Use cosine law to find the distance
63
Q

Cscx =

64
Q

1/sin =

65
Q

Secx=

66
Q

1/cosx =

67
Q

Cotx =

68
Q

1/tanx =

69
Q

Tanx =

70
Q

sinx/cosx =

71
Q

tan^2x =

A

sin^2x/cos^2x

72
Q

sin^2x/cos^2x =

73
Q

sin ^2x + cos^2x =

74
Q

1 =

A

sin ^2x + cos^2x

75
Q

sin^2x =

A

1 - cos^2x

76
Q

1 - cos^2x =

77
Q

cos^2x =

A

1 - sin^2x

78
Q

Tan x =

79
Q

Cot x = (cos&sin)

80
Q

Cscx =

81
Q

Secx =

82
Q

Cotx =

83
Q

sin ^2x + cos^2x =

84
Q

Tan^2x + 1 =

85
Q

cot^2x + 1 =

86
Q

Strategies when proving trigonometric identities
1.start with the more…

A

Start with the more complicated side

87
Q

Strategies when proving trigonometric identities
2.use…

A

Use Logical steps

88
Q

Strategies when proving trigonometric identities
3.

A

Try one identity at a time and see where it takes you

89
Q

Strategies when proving trigonometric identities:
4.
note

A

Note: only change a value of 1 to sin2 θ + cos2 θ as a last resort as this usually complicates things rather than simplifies them. Recall that a value of 1 can also be changed to sin/sin or cos/cos for the purpose of a common denominator

90
Q

Strategies when proving trigonometric identities:
5.
convert waht to ehat aleays

A

ii) Convert tanx to sinx/cosx always

91
Q

Strategies when proving trigonometric identities:
6. use algebra..

A

Use Algebra Skills
Expand
Find common denominator
Factor

92
Q

Strategies when proving trigonometric identities:
7.always keep an…

A

Always keep an eye on the other side

93
Q

On the test:
Question 1:

A

-Bearing of 195/155 with an angle of depression of 16degress/12
-0,90,180,270
- 50 m height
- 10 and 12-degree angles of depression
- Use cosine law
–c2 = a2 + b2 − 2ab cos(C)
–a2 = b2 + c2 - 2bccos(A)

94
Q

On the test:
Question 2:
no bc…

A

No because you need the other angle of depression from the other side in order to work out the side lengths that would then allow you to finally find the distance using cosine law

95
Q

On the test:
Question 3:

2tanx=√12

A

2tanx=√12
2tanx= √4√3
=2√3/2
=√3/1
=√3

96
Q

On the test:
Question 4:
angle 1 =
angle 2 =

A

Angle 1 = 60
Angle 2 = 240

97
Q

On the test:
Question 5:

Secxcscx = cotx + tanx

A

Secxcscx = cotx + tanx
Right side = 1/tanx + sinx/cosx
1 ➗sinx/cosx + sin/cosx
1 X cosx/sinx + sinx/cosx
cosx/sinx + sinx/cosx
cosxcosx/sincosx + sinxsinx/sinxcosx
Cos2x/sincosx + sin2x/sinxcosx
1/sinxcosx
(1/sin)(1/cos)
secxcsc

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