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MCR3U1 U4L1 TRIGONOMETRIC RATIOS (of ACUTE ANGLES) PART A ~ INTRODUCTION A. Labelling a Triangle A angles are labelled using upper case letters sides are labelled using lower case letters on the sides opposite the corresponding angles unknown angles are often labelled with the Greek letters, (theta), (alpha), (beta) B B. C Angles of Elevation and Depression The angle of elevation is the angle that the line of sight makes with an imaginary horizontal line while looking up. The angle of depression is the angle that the line of sight makes with an imaginary horizontal line while looking down. Angle of Elevation Angle of Depression Angle of Depression Angle of Elevation (angle of depression = angle of elevation) C. The Primary Trigonometric Ratios The primary trigonometric ratios only apply to a right–angled triangle. MCR3U1 U4L1 SOH CAH TOA sin opposite hypotenuse cos adjacent hypotenuse tan opposite adjacent PART B ~ EXAMPLES Ex Evaluate each of the following: a) Ex sin 150 b) , if cos = 0.5874 Determine the missing side to the nearest tenth of a unit. c) , if tan = 1.3787 Determine the missing angle to the nearest degree. 25m x 420 7m Ex 15m To solve a triangle means to determine all the unknown angles and side lengths. Solve ∆ABC, given b = 4.5 cm, c = 2.0 cm and ∠B = 90°. MCR3U1 U4L1 PART C ~ THE RECIPROCAL TRIGONOMETRIC RATIOS RECIPROCAL TRIG RATIOS 1 sin hypotenuse opposite 1 cos hypotenuse adjacent csc Ex sec 1 tan adjacent opposite cot Evaluate each of the following: a) csc 350 , if sec = 1.5874 b) c) , if cot = 1.4678 Given ∆ABC, state the six trigonometric ratios for A. Ex A 5 4 B Ex C 3 Use reciprocal trigonometric ratios to determine the value of the unknown: a) x 20cm 230 MCR3U1 U4L1 b) 7m 3m The angle of elevation to the top of a building is 740 from a point 65m from the base of the building. Calculate the height of the building, rounded to 1 decimal place. BUILDING Ex NOTE: The sine and cosine ratios are less than or equal to 1 so their reciprocal ratios, cosecant and secant, are always greater than or equal to 1. The tangent ratio can be less than 1, equal to 1, or greater than 1, so the reciprocal ratio, cotangent, can take on this range of values. HOMEWORK: p.280–282 #1–9, 11, 12