trigo 1

3 © 2009 - 2011 tutorco.com Pre-Cal/6/1/T Specific Objectives: . Student will be able to understand the concept of evaluating ratios based on right triangle trigonometry. TOPIC: INTRODUCTION TO TRIGONOMETRY AND ITS APPLICATIONS What they already know: The student knows the basics of angles , sides of a right triangle, pythogorean theorem. Suggested examples: Six Trigonometric Functions: sine of θ   =  sin θ   =    opposite  hypotenuse         cosecant of θ   =  csc θ   =  hypotenuse  opposite   cosine of θ   =  cos θ   =    adjacent  hypotenuse         secant of θ   =  sec θ   =  hypotenuse  adjacent   tangent of θ   =  tan θ   =  opposite adjacent         cotangent of θ   =  cot θ   =   adjacentopposite Notice that each ratio (function) in the right-hand column is theinverse ratio, or the reciprocal, of the ratio in the left-hand column. Key Concept: Plan of action: Evaluating ratios in right triangle trigonometry Finding the missing side/angles in a right triangle. The reciprocal of sin θ is csc θ ; and vice-versa. The reciprocal of cos θ is sec θ. And the reciprocal of tan θ is cot θ Example 1: In a right triangle, sin θ =   5 13 .  Sketch the triangle, place the ratio numbers, and evaluate the remaining functions of θ. Solution: To find the unknown side x, we have x² + 5² = 13² x² = 169 − 25 = 144 Therefore, x = √144 = 12.    We can now evaluate all six functions of θ: sin θ   =   5 13         csc θ   =  13 5  cos θ   =  1213         sec θ   =  1312 tan θ   =   5 12         cot θ   =  12 5  Example 2: In a right triangle, cos θ =  25 .  Sketch the triangle and evaluate sin θ. Solution: Example 3: Given cot θ = .  Sketch the triangle and evaluate csc θ. Solution: Example 4: Find the value of Cos 10° Solution: Using the scientific calculator the value of Cos 10° can be found out . Solution is 0.9848.