Trigonometry

Logarithm vs Natural Logarithm

• Logarithm is an inverse to an exponent

log39 = 2

• Natural logarithm has a special base or

e which equals 2.7813

Trigonometry

• Trigonometry means triangle measures

• Objective: calculate for the measure of a side or angle– We will be concentrating our studies on right

triangles

Trigonometric Functions

Opposite Hypotenuse

θ

Adjacent

Length of a side = opposite, hypotenuse, adjacentMeasurement of an angle = sin, cosine, tangentSin = opp/hyp Cos = adj/hypTan = opp/adjMeasurement of a side or angle is based on a ratio

Quick Example

17 21

θ

27

1. Sin – opp/hyp

21/27

2. Cos adj/hyp

17/27

3. Tan opp/adj

21/17

First assignment

• Unit 4.1 Page 227 Problems 1 - 8

Find a missing side length

53o

x

15

Step 1 sin53o = 15/x

Step 2 sin53ox = 15

Step 3 x = 15/sin53o

Step 4 = 18.8

Solve for the missing length

• 9 x• 21o

• Step 1: Identify sin, cosine, hypotenuse• Step 2: sin = 9, hypotenuse = x• Step 3: sin 21o = 9/x• Step 4: sin 21ox = 9• Step 5: x = 9/sin21o

• Step 6: x = 23.4

Problems

• Unit 4.1 Problems 19 - 24

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

Find a missing length

• Page 223 Guided practice 41. Diagram 48o

xft

75ft

2. Identify:Opposite = x ft; adjacent = 75ft

hypotenuse –not relevant

3. Solve tan48o = x/75

tan(48o)75 = x

83.3ft = x

First assignment

• Unit 4.1 Page 227 Problems 27 - 29

Find a missing angle measure

1. Review: acute angle is less than 90o

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

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-1θ = 14/16 → 61o

Find missing angle measurement

• See Page 223 – Guided practice 5b• 12 • θ • 5

• 1. θ is acute2.Side measuring 5 is adjacent; 12 represents

hypotenuse3.Cos-1θ = 5/12 → 65o

Problems

• Unit 4.1 Page 227 Problems 31 - 38

Angle of elevation

• angle of depression

• line of sight

• angle of elevation

•

• ground

Angle of elevation

• Page 224 guided practice 6

tan 36o = 1500/x

tan 36ox = 1500

x = 1500/tan 36o

x = 2065

Unit 4.1 Page 228 problem 39

Solve a right triangle

• A 37 C

• 20

• B

• SinA-1 = 20/37 →• <C = 36• Tan = 20/c

Solve a right triangle

• Unit 4.1 Page 228 Problems 47 - 50