00 90 180 270 360 the 4 quadrants 1st quadrant2nd quadrant 4th quadrant 3rd quadrant
TRANSCRIPT
0
90
180
270
360
The 4 quadrants
1st quadrant2nd quadrant
4th quadrant3rd quadrant
Representing Angles
45°
Measure from + x-axisAnti Clockwise Direction for +ve anglesCW Direction for –ve angles
Representing Angles
45°
−45°
Measure from + x-axisAnti Clockwise Direction for +ve anglesCW Direction for –ve angles
Representing Angles
135°
−135°
Measure from + x-axisAnti Clockwise Direction for +ve anglesCW Direction for –ve angles
Representing Angles
Measure from + x-axisAnti Clockwise Direction for +ve anglesCW Direction for –ve angles
225°
−225°
Special Angles
Equilateral Δ
- equal lengths
- equal angles
60
Assume each length is 2 units,
look at half of the Δ.
30
1
2
312 22
60
30
1
23
Special Angles
2
130sin
2
330 cos
3
130tan
2
360sin
2
160 cos
360tan
Special Angles
isosceles Δ
- equal arms
- equal base angles 45
1
12
2
145sin
2
145 cos 145tan
Assume each arm is 1 unit.
0
90
180
270
360
The 4 quadrants
1st quadrant2nd quadrant
4th quadrant3rd quadrant
sin +cos +tan +
sin +cos −tan −
sin −cos −tan +
sin −cos +tan −
0
90
180
270
360
The 4 quadrants
1st quadrant2nd quadrant
4th quadrant3rd quadrant
A all +S sin +
T tan + C cos +
0
901st quadrant
30°
1sin 30
2
3cos 30
2
1tan 30
3
12
3
902nd quadrant
30°
1sin 30
2
3cos 30
2
1tan 30
3
1801
2
3
3rd quadrant
30°
1sin 30
2
3cos 30
2
1tan 30
3
180
270
−12
3
4th quadrant
30°
1sin 30
2
3cos 30
2
1tan 30
3
270
360−12
3
Example 1
1cos 60
2
sin 240
cos 240
tan 240
60°
1
2
Step 1: Find the unknown length and determine sin 60° and tan 60 °
3
3sin 60
2
tan 60 3
o 3
2
240°
Step 2: Find the basic angle for 240° and determine the quadrant its in.
B.A = 60°
1
2
3
Example 2
tan 45 1
sin 315
cos 315
tan 315
Step 1: Find the unknown length and determine sin 45° and cos 45 °
45°
1
1
1sin 45
21
cos 452
o
1
2
315°
Step 2: Find the basic angle for 315° and determine the quadrant its in.
B.A = 45°
1
2
1
2
Exercise Q1
(a) sin 230 ( )
(b) cos 140 ( )
(c) tan 215 ( )
(d) cos 350 ( )
(e) tan 340 ( )
(f) sin 160 ( )
(g) cos ( 60 ) ( )
(h) tan ( 155 ) ( )
Exercise Q2
(a) tan 0 1st, 3rdA
(b) cos 0 and sin 0 4thA A
(c) cos and tan are same sign 1st, 2ndA A
(d) sin and tan are opposite sign 2nd, 3rdA A
Find the angles between 0 and 360 inclusive which satisfy
sin x = 0.7425Answer:
sin x = 0.7425
basic angle = 47.94 x = 47.9 or x = 180 - 47.94
= 132.06
or 132.1
tan x = −1.37Answer: (1st step: find B.A for tan x = 1.37)
basic angle = 53.87
x = 180 − 53.87 = 126.13
or x = 360 − 53.87 = 306.13
x = 126.1 or 306.1
Find the angles between 0 and 360 inclusive which satisfy
cos (x − 27) = − 0.145
Answer:
0 < x < 360
− 27 < x − 27 < 333
basic angle = 81.66
x − 27 = 180 − 81.66 = 98.34 x = 125.34
or x − 27 = 180 + 81.66 = 261.66 x = 288.66
x = 125.3 or 288.7
Find the angles between 0 and 360 inclusive which satisfy