Functions for Angles Between 0° and 90°
Common Values of Sin, Cos and Tan
Functions for Angles of Any Size
● Imagine triangle with hypotenuse h
● Opposite side = h sin θ
● Adjacent side = h cos θ
The Angles of Trigonometric Functions
● Imagine a triangle inside a circle with 4 quadrants
● Quadrant 1 0 < θ < 90, Quadrant 2 90 < θ < 180 etc.
● In the first quadrant, sin cos and tan are all positive
● In the second quadrant, only sin is positive
● In the third quadrant, only tan is positive
● In the fourth quadrant, only cos is positive
Trigonometric Graphs
Trigonometric Identities 1
Principle Values
● There are infinitely answers to an equation such as sin θ = 0.5 because the
sin graph continues forever
● Using a calculator will give a single value – the principle value
● Find other roots by looking at the symmetry of the graphs:
○ sin → 180 – principle value
○ cos → 360 – principle value
○ tan → 180 + principle value (or principle value – 180)
Solving Trigonometric Equations
● If given an equation in the form sin nx = k for a certain range, multiply the
range by n to get all values of x
● Rearrange to make sin, cos or tan the subject
● If quadratic, factorise if possible or use quadratic formula
● Use the identities seen above
Other Useful Formulae