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Trigonometry

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Logarithm vs Natural Logarithm Logarithm is an inverse to an exponent log 3 9 = 2 Natural logarithm has a special base or e which equals 2.7813

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Trigonometry Trigonometry means triangle measures Objective: calculate for the measure of a side or angle –We will be concentrating our studies on right triangles

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Trigonometric Functions Opposite Hypotenuse θ Adjacent Length of a side = opposite, hypotenuse, adjacent Measurement of an angle = sin, cosine, tangent Sin = opp/hypCos = adj/hyp Tan = opp/adj Measurement of a side or angle is based on a ratio

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Quick Example 17 21 θ 27 1.Sin – opp/hyp 21/27 2.Cos adj/hyp 17/27 3.Tan opp/adj 21/17

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First assignment Unit 4.1 Page 227 Problems 1 - 8

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Find a missing side length 53 o x 15 Step 1sin53 o = 15/x Step 2sin53 o x = 15 Step 3 x = 15/sin53 o Step 4 = 18.8

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Solve for the missing length 9 x 21 o Step 1: Identify sin, cosine, hypotenuse Step 2: sin = 9, hypotenuse = x Step 3: sin 21 o = 9/x Step 4: sin 21 o x = 9 Step 5: x = 9/sin21 o Step 6: x = 23.4

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Problems Unit 4.1 Problems 19 - 24

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Practical Trigonometry Directions for finding a missing length Diagram the situation –Just like Geometry Identify the hypotenuse, opposite and adjacent sides and the angle Solve for the missing length

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Find a missing length Page 223 Guided practice 4 1.Diagram 48 o x ft 75ft 2. Identify:Opposite = x ft; adjacent = 75ft hypotenuse –not relevant 3. Solve tan48 o = x/75 tan(48 o) 75 = x 83.3ft = x

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First assignment Unit 4.1 Page 227 Problems 27 - 29

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Find a missing angle measure 1.Review: acute angle is less than 90 o 2.If θ is an acute angle and the of sine of θ is x (unknown), then sin -1 x = θ 1.This is true for tangent and cosine See Page 223 – Guided practice 5a

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Find a missing angle measure See Page 223 – Guided practice 5a 14 θ 16 1.θ is acute 2.Side measuring 14 is sine; 16 represent hypotenuse 3.Sin -1 θ = 14/16 → 61 o

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Find missing angle measurement See Page 223 – Guided practice 5b 12 θ 5 1.θ is acute 2.Side measuring 5 is adjacent; 12 represents hypotenuse 3.Cos -1 θ = 5/12 → 65 o

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Problems Unit 4.1 Page 227 Problems 31 - 38

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Angle of elevation angle of depression line of sight angle of elevation ground

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Angle of elevation Page 224 guided practice 6 tan 36 o = 1500/x tan 36 o x = 1500 x = 1500/tan 36 o x = 2065 Unit 4.1 Page 228 problem 39

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Solve a right triangle A 37 C 20 B SinA -1 = 20/37 → <C = 36 Tan = 20/c

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Solve a right triangle Unit 4.1 Page 228 Problems 47 - 50

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