Activity 4 2 Trig Ratios of Any Angles

Activity 4 -2: Trig Ratios of Any Angles Part 3: Exact Values of the Trigonometric and Reciprocal Trigonometric Ratios for Special Angles

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: 45 o or π/4 Acute Angle with a Radius of √ 2 Primary Ratio y (1, 1) √ 2 Reciprocal Ratio Sine Ratio sin(π/4) = 1/√ 2 Cosecant Ratio csc (π/4) = √ 2 Cosine Ratio cos(π/4) = 1/√ 2 Secant Ratio sec (π/4) = √ 2 Tangent Ratio tan(π/4) = 1/1 =1 Cotangent Ratio cot (π/4) = 1/1 =1 1 θ= π/4 1 x

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: 30 o or π/6 Acute Angle with a Radius of 2 Primary Ratio y (√ 3, 1) 2 √ 3 Sine Ratio sin(π/6) = 1/2 Cosecant Ratio csc (π/6) = 2 Cosine Ratio cos(π/6) = √ 3/2 Secant Ratio sec (π/6) = 2/√ 3 Tangent Ratio tan(π/6) = 1/√ 3 =1 Cotangent Ratio cot (π/6) = √ 3/1 = √ 3 1 1 θ= π/6 Reciprocal Ratio x

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: 60 o or π/3 Acute Angle with a Radius of 2 Primary Ratio y (1, √ 3) 2 Reciprocal Ratio Sine Ratio sin(π/3) = √ 3/2 Cosecant Ratio csc (π/3) = 2/√ 3 Cosine Ratio cos(π/3) = 1/2 Secant Ratio sec (π/3) = 2/1 = 2 Tangent Ratio tan(π/3) = √ 3/1 = √ 3 Cotangent Ratio cot (π/3) = 1/√ 3 θ= π/3 1 x

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 θ=5π/3 Primary Ratio y π/3 2π/3 1 3π/3 x -√ 3 2 4π/3 (1, -√ 3) θ= 5π/3 Related Acute Angle=π/3 Reciprocal Ratio Sine Ratio sin(π/3) = -√ 3/2 Cosecant Ratio csc (π/3) = -2/√ 3 Cosine Ratio cos(π/3) = 1/2 Secant Ratio sec (π/3) = 2/1 = 2 Tangent Ratio tan(π/3) = -√ 3/1 = -√ 3 Cotangent Ratio cot (π/3) = -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 Example 2: Find all the possible angles between 0≤θ≤ 2π for the following: cot θ=-1/√ 3 y Since the ratio is negative, the angle resides in Quadrant 2 and Quadrant 4 cot θ = x/y = -1/√ 3. : x = 1 or -1. : y = √ 3 or -√ 3 θ= 2π/3 √ 3 1 x -1 5π/3 -√ 3 When x = -1 and y = √ 3, the angle that is formed is 2π/3 When x = 1 and y = -√ 3, the angle that is formed is 5π/3 The possible angles for cotθ=-1/√ 3 are: θ = 2π/3 and θ = 5π/3

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.