The 4 quadrants 90 2nd quadrant 1st quadrant 0 180 360

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Presentation transcript:

The 4 quadrants 90 2nd quadrant 1st quadrant 0 180 360 3rd quadrant 4th quadrant 270

Representing Angles 45° Measure from + x-axis Anti Clockwise Direction for +ve angles CW Direction for –ve angles

Representing Angles 45° −45° Measure from + x-axis Anti Clockwise Direction for +ve angles CW Direction for –ve angles

Representing Angles 135° −135° Measure from + x-axis Anti Clockwise Direction for +ve angles CW Direction for –ve angles

Representing Angles 225° −225° Measure from + x-axis Anti Clockwise Direction for +ve angles CW Direction for –ve angles

Special Angles 2 1 Equilateral Δ - equal lengths - equal angles 30 60 1 Assume each length is 2 units, look at half of the Δ.

Special Angles 60 30 1 2

Special Angles 1 1 isosceles Δ - equal arms - equal base angles 45 Assume each arm is 1 unit.

The 4 quadrants 90 2nd quadrant 1st quadrant 0 180 360 sin + cos − tan − sin + cos + tan + 0 180 360 sin − cos − tan + sin − cos + tan − 3rd quadrant 4th quadrant 270

S sin + A all + T tan + C cos + The 4 quadrants 90 2nd quadrant 1st quadrant S sin + A all + 0 180 360 T tan + C cos + 3rd quadrant 4th quadrant 270

1st quadrant 90 1 2 0 30°

2nd quadrant 90 2 1 30° 180

3rd quadrant 180 30° −1 2 270

4th quadrant 360 30° −1 2 270

Example 1 60° 1 2 Step 1: Find the unknown length and determine sin 60° and tan 60 ° 240° B.A = 60° Step 2: Find the basic angle for 240° and determine the quadrant its in.

Example 2 45° 1 Step 1: Find the unknown length and determine sin 45° and cos 45 ° 315° B.A = 45° Step 2: Find the basic angle for 315° and determine the quadrant its in.

Exercise Q1

Exercise Q2

Find the angles between 0 and 360 inclusive which satisfy sin x = 0.7425 Answer: sin x = 0.7425 basic angle = 47.94  x = 47.9 or x = 180 - 47.94 = 132.06 or 132.1

Find the angles between 0 and 360 inclusive which satisfy tan x = −1.37 Answer: (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