Activity 4-2: Trig Ratios of Any Angles

1
Activity 4-2 Trig Ratios of Any Angles

• Part 3 Exact Values of the Trigonometric and
  Reciprocal Trigonometric Ratios for Special Angles

2
Activity 4-2 Trig Ratios of Any Angles

• Part 3 Exact Values of the Trigonometric and
  Reciprocal Trigonometric Ratios for Special Angle

• Let us review some special cases

CASE 1 45o or p/4 Acute Angle with a Radius of v2
Reciprocal Ratio
Primary Ratio
Sine Ratio sin(p/4) 1/v2
Cosecant Ratio csc (p/4) v2
(1, 1)
v2
1
Cosine Ratio cos(p/4) 1/v2
Secant Ratio sec (p/4) v2
? p/4
1
Tangent Ratio tan(p/4) 1/1 1
Cotangent Ratio cot (p/4) 1/1 1
3
Activity 4-2 Trig Ratios of Any Angles
Part 3 Exact Values of the Trigonometric and
Reciprocal Trigonometric Ratios for Special Angle

• Let us review some special cases

CASE 2 30o or p/6 Acute Angle with a Radius of 2
Reciprocal Ratio
Primary Ratio
Sine Ratio sin(p/6) 1/2
Cosecant Ratio csc (p/6) 2
(v3, 1)
1
2
1
Cosine Ratio cos(p/6) v3/2
Secant Ratio sec (p/6) 2/v3
? p/6
v3
Tangent Ratio tan(p/6) 1/v3 1
Cotangent Ratio cot (p/6) v3/1 v3
4
Activity 4-2 Trig Ratios of Any Angles
Part 3 Exact Values of the Trigonometric and
Reciprocal Trigonometric Ratios for Special Angle

• Let us review some special cases

CASE 3 60o or p/3 Acute Angle with a Radius of 2
Reciprocal Ratio
Primary Ratio
(1, v3)
Sine Ratio sin(p/3) v3/2
Cosecant Ratio csc (p/3) 2/v3
2
v3
Cosine Ratio cos(p/3) 1/2
Secant Ratio sec (p/3) 2/1 2
? p/3
1
Tangent Ratio tan(p/3) v3/1 v3
Cotangent Ratio cot (p/3) 1/v3
5
Activity 4-2 Trig Ratios of Any Angles
Part 3 Exact Values of the Trigonometric and
Reciprocal Trigonometric Ratios for Special Angle

• Let us review some special cases

Example 1 Find the EXACT value of all of the
trigonometric ratios for ?5p/3
Reciprocal Ratio
Primary Ratio
p/3
2p/3
Sine Ratio sin(p/3) -v3/2
Cosecant Ratio csc (p/3) -2/v3
Cosine Ratio cos(p/3) 1/2
Secant Ratio sec (p/3) 2/1 2
1
3p/3
-v3
Tangent Ratio tan(p/3) -v3/1 -v3
Cotangent Ratio cot (p/3) -1/v3
2
(1, -v3)
4p/3
? 5p/3
Related Acute Anglep/3
6
Activity 4-2 Trig Ratios of Any Angles
Part 3 Exact Values of the Trigonometric and
Reciprocal Trigonometric Ratios for Special Angle

• Let us review some special cases

Example 2 Find all the possible angles between
0?2p for the following cot ?-1/v3
Since the ratio is negative, the angle resides in
Quadrant 2 and Quadrant 4
cot ? x/y -1/v3 . x 1 or -1 . y v3 or
-v3
? 2p/3
v3
1
When x -1 and y v3, the angle that is formed
is 2p/3
-1
-v3
When x 1 and y -v3, the angle that is formed
is 5p/3
5p/3
The possible angles for cot?-1/v3 are ? 2p/3
and ? 5p/3
7
Activity 4-2 Trig Ratios of Any Angles
Part 3 Exact Values of the Trigonometric and
Reciprocal Trigonometric Ratios for Special Angle

• You have completed this presentation, go back to
  the activity page and complete the rest of the
  lesson.