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Flashcards in Trigonometry Deck (47):
1

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

  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

2

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

  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

3

Find tan 7π/4

  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

4

Qadrants: 30, 700, 5π/3 and - 3π/5

 

  1. 30: Quadrant 1
  2. 700 : Q IV
  3. 5π/3 : Q IV
  4. - 3π/5: Q III

5

sin(30 )

1/2

6

sin(45)

sqrt(2) /2

7

sin 60

sqrt(3) / 2

8

sin 90

1

9

sin 120

sqrt(3) / 2

 

10

sin 135

sqrt(2) / 2

11

sin 150

1/2

12

sin 180

0

13

sin 210

- 1/2

14

sin 225

-sqrt(2) / 2

15

sin 240

- sqrt (3) / 2

16

sin 270

-1

17

sin 300

- sqrt(3) / 2

18

sin 315

- sqrt(2) / 2

19

sin 330

- 1/2

20

sin 360

= sin 0 = 0

21

cos 0 

1

22

cos 30

sqrt(3) / 2

23

cos 45

sqrt(2) / 2

24

cos (60)

1/2

25

cos 90 

0

26

cos 120

- 1/2

27

cos 135

- sqrt(2) / 2

28

cos  150

- sqrt(3) / 2

29

cos 180

-1

30

cos 210

- sqrt(3) / 2

31

cos (225)

- sqrt(2) / 2

32

cos(240)

- 1 /2

33

cos 270

0

34

cos 300

1/2

35

cos 315

sqrt(2) / 2

36

cos (330)

sqrt(3) / 2

37

cos 360

= cos 0 = 1

38

pi/6 radians

30 degrees

39

pi/3 radians

60 degrees

 

40

π / 4 radians

45o

41

π / 2 radians

90o

42

2 π/3

120 degrees

43

Determine sin 300

Quadrant ==> IV

- sqrt(3) / 2

44

csc 150 

1 / sin

==> 1 / (sin 150)

== 1 / sin(30)

== 2

45

cot 5π/3

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

signs of cos theta

and sin thetha

given theta?

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

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

47

find sin(105)

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