Trigonometry Flashcards
1
Q
Find angles between 0 and 360 degrees which are the same as -Π/2, 1180oand 9Π/4
A
- The first is negative so we add 2Π.
- -Π/2 + 2Π = 3Π/2
- 1180o = 11800 - 3600 = 8200 = 4600 = 100o
- 9Π/4 radians = 9 Π/4 - 2Π radians= Π/4 radians
2
Q
How do we find the CosΘ and sinΘ are for arbitrary Θ ?
A
- Determine the quadrant.
- Draw right triangle by drawing an altitude to the the x axis.
- Get the Cartesian co-ordinates (x,y).
- Points to the left of the y axis have a negative * x* and those below have a negative y.
- we then set sin Θ = x
- and cos Θ = y
3
Q
Find tan 7π/4
A
- Determine quadrant – since 7π/4 is greater than 3π/2 and less than 2π, the angle is in the fourth quadrant.
- Draw altitude.
- Determine the acute angle which is: π/4
- cos π/4 = sqrt(2)/2 as is sin π/4.
- 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.
- tan 7π/4 = (sin 7π/4 )/ (cos 7π/4) = -1
4
Q
Qadrants: 30, 700, 5π/3 and - 3π/5
A
- 30: Quadrant 1
- 700 : Q IV
- 5π/3 : Q IV
- 3π/5: Q III
5
Q
sin(30 )
A
1/2
6
Q
sin(45)
A
sqrt(2) /2
7
Q
sin 60
A
sqrt(3) / 2
8
Q
sin 90
A
1
9
Q
sin 120
A
sqrt(3) / 2
10
Q
sin 135
A
sqrt(2) / 2
11
Q
sin 150
A
1/2
12
Q
sin 180
A
0
13
Q
sin 210
A
- 1/2
14
Q
sin 225
A
-sqrt(2) / 2
15
Q
sin 240
A
- sqrt (3) / 2
16
Q
sin 270
A
-1
17
Q
sin 300
A
- sqrt(3) / 2
18
Q
sin 315
A
- sqrt(2) / 2