Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lesson 4: Evaluating Trigonometric Ratios for Any Angle Between 0 and 360 (Part 1) Part A – Definitions CAST rule: An easy way to indicate the trigonometric ratios that are POSITIVE in the four quadrants. Example 1: Determining the trigonometric ratio given an obtuse angle. Procedure: find the related acute angle use special triangles, to determine the exact ratio go back to the original, principal angle and use the CAST rule to determine whether your answer is positive or negative NOTE: The CAST rule helps you to remember which trigonometric ratios are positive in each quadrant. S A T C Evaluate. Leave answer as an exact value where appropriate. a) tan 150 b) sin 225 c) cot 120 d) cos 330 e) csc 240 f) sin 315 Part B – Trig. Ratios for Angles Between 0 and 360 Key Idea: The trig. ratios for any principal angle, θ , in standard position, where 0 θ 360 , can be determined by finding the related acute angle using coordinates of any point P (x , y ) that lies on the terminal arm of the angle. Example 2: The point P (3, 4) lies on the terminal arm of an angle θ in standard position. a) Sketch the angle. b) Determine the exact ratio for sin θ , cosθ , and tan θ . c) Repeat the above steps for points (3, 4) , (3, 4) , and (3, 4) . QII Sine y QI All (3, 4) θ x Tangent QIII Cosine QIV Example 3: The P (5, 12) lies on the terminal arm of angle θ in standard position. a) Determine the exact values of sin θ , cosθ , and tanθ . b) State the value of θ . y x Worksheet: Trig. Ratios for Angles Between 0 and 360 Evaluate. Leave answer as an exact value where appropriate. a) cos155 b) sin 214 c) tan 315 d) cos 240 e) cot 150 f) cos 225 g) sin 300 h) sec 330 Answers: a) 0.9063 b) 0.5592 c) -1 e) 3 f) 2 2 g) d) 3 2 h) 1 2 2 3