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Higher Mathematics > 5. Trig Equations > Flashcards

5. Trig Equations Flashcards

1
Q

Method for basic trig equations

A
  1. Rearrange so operation (cos, tan, sin) is on its own
  2. Use triangles
  3. CAST
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2
Q

Solve 4 cosx - 5 = -3, 0 < x < 360

A

x = 60, 300

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3
Q

solve /2 sinx - 1 = 0, 0 < x < 720

A

x = 45, 135, 405, 495

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4
Q

What to do when interval is >360

A

Add 360 to solutions until it exceeds 720

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5
Q

Method when there is a multiple angle

A
  1. Alter the interval
  2. Calculate the first 2 values
  3. Find all values by +360, remaining within interval
  4. Divide answers so left with x = solutions
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6
Q
  1. Alter the interval
  2. Calculate the first 2 values
  3. Find all values by +360, remaining within interval
  4. Divide answers so left with x = solutions
A

Method when there is a multiple angle

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7
Q

Multiple angle =

A

Number in front of x

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8
Q

Solve sin3x = -0.8, 0 < 3x < 360. calculator

A

77.7, 102.3, 197.7, 223.3, 317.7, 342.3

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9
Q

Solve 4 = 5 - tan2x, 0 < x < 360

A

x = 22.5, 112.5, 202.5, 292.5

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10
Q

Solve 4cos^2x - 5 = -2, 0 < x < 360

A

x = 30, 150, 210, 330

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11
Q

What to do if operation (cos, tan, sin) is both +ive and -ive

A

Use all four quadrants

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12
Q

When is a operation (cos, tan, sin) both positive and negative

A

When it is equal to a square root

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13
Q

Solve 4sin^2x + 11sinx + 6 = 0 (calc)

A

228.59, 311.41

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14
Q

Solve 2cos^2x = 5 - 7sinx, 0 < x < 360

A

x = 30 or 150

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15
Q

Sin and cos relationships

A

sin^2x + cos^2x = 1

sin^2x = 1 - cos^2x

cos^2x = 1 - sin^2x

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16
Q

Solve sin (2x - 20) = 0.5, 0 < x < 360

A

x = 25, 85, 205, 265

17
Q

pi radians in degrees

18
Q

Maximum value on a trig graph

A

Largest value

19
Q

Minimum valence on a trig graph

A

Smallest value

20
Q

Period

A

Length of one cycle of the wave

21
Q

Length of one cycle of the wave

22
Q

Amplitude

A

Distance from middle of graph to top of graph

23
Q

Distance from middle of graph to top of graph

24
Q

Exact value triangles

25
Q

Exact value of sin30

26
Q

If angle is a multiple of 90, what do you use

27
Q

Method for finding exact value of an angle

A

Convert angle to degrees

Find quadrant (CAST) and sign

Write angle (distance from 180 or 360)

Use triangles to find exact value

28
Q

Find exact value of sin150

29
Q

Exact value of sin300

30
Q

Exact value of cos 3 pi / 4

31
Q

Exact value of sin 11pi / 4

32
Q

solve 3cos (2x + pi/4) = 1 for 0 < x < pi
(calc)

A

adjusted interval = 405

x = 12.765, 122.235

Higher Mathematics (11 decks)

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