Trigonometry
Functions for Angles Between 0° and 90°
opp
sin θ = hyp
adj
cos θ = hyp
opp
tan θ = adj
cos θ = sin(90° − θ)
sin θ = cos(90° − θ)
Common Values of Sin, Cos and Tan
0° 30° 45° 60° 90°
sin 0 1 √2 √3 1
2 2 2
cos 1 √3 √2 1 0
2 2 2
tan 0 √3 1 √3 N/A
3
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
Courtesy of National 5 Maths
Functions for Angles Between 0° and 90°
opp
sin θ = hyp
adj
cos θ = hyp
opp
tan θ = adj
cos θ = sin(90° − θ)
sin θ = cos(90° − θ)
Common Values of Sin, Cos and Tan
0° 30° 45° 60° 90°
sin 0 1 √2 √3 1
2 2 2
cos 1 √3 √2 1 0
2 2 2
tan 0 √3 1 √3 N/A
3
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
Courtesy of National 5 Maths
