Lesson 1: Trigonometric Functions of Acute Angles Done by: Justin Lo Lee Bing Qian Danyon Low Tan Jing Ling

Trigonometric Functions The three main functions in trigonometry are Sine, Cosine and Tangent. They are often shortened to sin, cos and tan.

Using your calculator… Use the calculator to find the following

Sin, Cos, Tan Let this angle be x Opposite Hypotenuse Adjacent

Let this angle be x Opposite Hypotenuse Adjacent "Opposite" is opposite to the angle x "Adjacent" is adjacent (next to) to the angle x "Hypotenuse" is the longest line Sine Function:sin(x) = Opposite / Hypotenuse Cosine Function:cos(x) = Adjacent / Hypotenuse Tangent Function:tan(x) = Opposite / Adjacent SOH CAH TOA

Example 1: Line A = cm Line B (Hypotenuse) = 2 cm Line C = 1 cm Solution: Length of Line C (Opposite) Length of Line B (Hypotenuse)

Example 2: Line A = cm Line B (Hypotenuse) = 2 cm Line C = 1 cm Line C is adjacent to angle Length of Line C (Adjacent) Length of Line B (Hypotenuse) Recall the formula: Solution:

Example 3: Solution: Line A = 1 cm Line C = 1 cm Length of Line A/C (Opposite) Length of Line C/A (Adjacent)

AngleRatio (AC:CB:BA)Sine(x)Cosine(x)Tangent(x)

Note: Always draw a diagram to visualise if confused! What if the triangle is not right-angled? Can we still use sin, cos, tan? – Angle of reference – Applies to adjacent and opposite too – Dependent on angle not triangle

Think… How far up a wall could Bob the Builder reach with a 30 foot ladder, if the ladder makes a 70° angle with the ground? (2d.p) y 30

Refer to Worksheet

Inverse Trigonometric Functions Just as the square root function is defined such that y 2 = x, the function y = arcsin(x) is defined so that sin(y) = x NameUsual Notation DefinitionAka ArcsineY = arcsin xX= sin y ArccosineY= arccos xX= cos y ArctangentY= arctan xX= tan y

False!

Example 4: 4cm 5 cm 3 cm Solution: x

Example 5: 12cm 13 cm 5 cm Solution: x

Example 6: 12cm 13 cm 5 cm Solution: x

WORKSHEET TIME!