Trigonometry Flashcards

1
Q

Find angles between 0 and 360 degrees which are the same as -Π/2, 1180oand 9Π/4

A
  1. The first is negative so we add 2Π.
    1. -Π/2 + 2Π = 3Π/2
  2. 1180o = 11800 - 3600 = 8200 = 4600 = 100o
  3. 9Π/4 radians = 9 Π/4 - 2Π radians= Π/4 radians
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2
Q

How do we find the CosΘ and sinΘ are for arbitrary Θ ?

A
  1. Determine the quadrant.
  2. Draw right triangle by drawing an altitude to the the x axis.
  3. Get the Cartesian co-ordinates (x,y).
  4. Points to the left of the y axis have a negative * x* and those below have a negative y.
  5. we then set sin Θ = x
  6. and cos Θ = y
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3
Q

Find tan 7π/4

A
  1. Determine quadrant – since 7π/4 is greater than 3π/2 and less than 2π, the angle is in the fourth quadrant.
  2. Draw altitude.
  3. Determine the acute angle which is: π/4
  4. cos π/4 = sqrt(2)/2 as is sin π/4.
  5. Determine sign: since the angle is in the fourth quadrant and x is positive and y is negative, so cos 7π/4 is positive and sin 7π/4 is negative.
  6. tan 7π/4 = (sin 7π/4 )/ (cos 7π/4) = -1
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4
Q

Qadrants: 30, 700, 5π/3 and - 3π/5

A
  1. 30: Quadrant 1
  2. 700 : Q IV
  3. 5π/3 : Q IV
    • 3π/5: Q III
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5
Q

sin(30 )

A

1/2

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6
Q

sin(45)

A

sqrt(2) /2

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7
Q

sin 60

A

sqrt(3) / 2

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8
Q

sin 90

A

1

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9
Q

sin 120

A

sqrt(3) / 2

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10
Q

sin 135

A

sqrt(2) / 2

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11
Q

sin 150

A

1/2

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12
Q

sin 180

A

0

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13
Q

sin 210

A
  • 1/2
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14
Q

sin 225

A

-sqrt(2) / 2

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15
Q

sin 240

A
  • sqrt (3) / 2
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16
Q

sin 270

A

-1

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17
Q

sin 300

A
  • sqrt(3) / 2
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18
Q

sin 315

A
  • sqrt(2) / 2
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19
Q

sin 330

A
  • 1/2
20
Q

sin 360

A

= sin 0 = 0

21
Q

cos 0

A

1

22
Q

cos 30

A

sqrt(3) / 2

23
Q

cos 45

A

sqrt(2) / 2

24
Q

cos (60)

A

1/2

25
Q

cos 90

A

0

26
Q

cos 120

A
  • 1/2
27
Q

cos 135

A
  • sqrt(2) / 2
28
Q

cos 150

A
  • sqrt(3) / 2
29
Q

cos 180

A

-1

30
Q

cos 210

A
  • sqrt(3) / 2
31
Q

cos (225)

A
  • sqrt(2) / 2
32
Q

cos(240)

A
  • 1 /2
33
Q

cos 270

A

0

34
Q

cos 300

A

1/2

35
Q

cos 315

A

sqrt(2) / 2

36
Q

cos (330)

A

sqrt(3) / 2

37
Q

cos 360

A

= cos 0 = 1

38
Q

pi/6 radians

A

30 degrees

39
Q

pi/3 radians

A

60 degrees

40
Q

π / 4 radians

A

45o

41
Q

π / 2 radians

A

90o

42
Q

2 π/3

A

120 degrees

43
Q

Determine sin 300

A

Quadrant ==> IV

  • sqrt(3) / 2
44
Q

csc 150

A

1 / sin

==> 1 / (sin 150)

== 1 / sin(30)

== 2

45
Q

cot 5π/3

A

Quadrant IV

cot(-π/3)

cot (- π/3)

  • sqrt(3) / 3

cos(π/3) = 1/2

cot(π/3) [=] 1/3sqrt(3)

csc(π/3) = 2/3sqrt(3)
(7)
[sec(pi/3)] [=] [2]
(8)
[sin(pi/3)] [=] [1/2sqrt(3)]
(9)
[tan(pi/3)] [=] [sqrt(3).]

46
Q

signs of cos theta

and sin thetha

given theta?

A

cos is positive in I,IV, negative in II, III

sin is positive in I, II, negative in III, IV

47
Q

find sin(105)

A

What is the exact value of sin(105º)?

We can use a sum angle formula noticing that 105º = 45º + 60º.

We have sin(105º) = sin(45º + 60º) = sin(45º )cos(60º) + cos(45º )sin(60º).

We know the exact values of trig functions for 60º and 45º.

Therefore, sin(45º )cos(60º) + cos(45º )sin(60º)

(sqrt(2) + sqrt(6))/4