Done by: Chew Tian Le (2i302) Lee Liak Ghee (2i310) Low Wei Yang (2i313)- Leader Ng Shen Han (2i316)

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Done by: Chew Tian Le (2i302) Lee Liak Ghee (2i310) Low Wei Yang (2i313)- Leader Ng Shen Han (2i316)

Agenda Introduction to trigonometry- Right-angled triangles, theta, etc. Trigonometric functions Angle of elevation Angle of depression Applicability in real life Simple problems involving angles of elevation/depression

Introduction to Trigonometry  Formed from Greek words 'trigonon' (triangle) and 'metron' (measure).  Trigonometric triangles are always right- angled triangles

More on Trigonometry Triangles Relationship between sides and angles between sides A branch of mathematics that studies Describes relationship between sides/angles Uses trigonometric functions

Sides of a Right-angled Triangle Opposite to the right-angle Longest side Hypotenuse Side that touches θ Adjacent Side opposite to θ Opposite

Theta  8 th letter of the Greek alphabet  Represented by “ θ ”  A variable, not a constant  Commonly used in trigonometry to represent angle values

Trigonometric Functions  Sin (Sine)= ratio of opposite side to the hypotenuse  Cos (Cosine)= ratio of adjacent side to the hypotenuse  Tan (Tangent)= ratio of opposite side to the adjacent side

Easier way to remember Sin, Tan, Cos  TOA CAH SOH (Big foot auntie in Hokkien)  TOA: Tangent = Opposite ÷ Adjacent (T=O/A)  CAH: Cosine = Adjacent ÷ Hypotenuse (C=A/H)  SOH: Sine = Opposite ÷ Hypotenuse (S=O/H)

Trigonometric Functions

Angle of Elevation  The angle of elevation is the angle between the horizontal line and the observer’s line of sight, where the object is above the observer

Angle of Depression  The angle of depression is the angle between the horizontal line and the observer’s line of sight, where the object is below the observer

Applicability of Angles of Elevation and Depression  Used by architects to design buildings by setting dimensions  Used by astronomers for locating apparent positions of celestial objects  Used in computer graphics by designing 3D effects properly  Used in nautical navigations by sailors (sextants)  Many other uses in our daily lives

Simple Word Problem involving Angles of Elevation  Little Tom, who is 0.75 metres tall is looking at a bug on the top of a big wall, which is 11 times his height. He is standing 2 metres away from the wall. What angle is he looking up at?  Solution: Actual height of ceiling: 0.75m x (11)= 8.25m Subtract off his own body height: 8.25m - 0.75m = 7.5m tan(θ) = 7.5m ÷ 2m tan -1 (7.5 ÷ 2) = 75.1... o

Simple Word Problem involving Angles of Depression  A boy 1m tall is standing on top of a staircase 33m high while looking at a patch of grass on the ground 50m away from him. Find the angle from which he is looking at.  Solution: Actual height boy is looking from: 33m + 1m = 34m sin(θ) = 34m ÷ 50m sin -1 (34 ÷ 50) = 42.8... o

Overall summary Draw the diagram Identify the known values Form equations Solve

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