TRIGONOMETRY AND GEOMETRY 
Remember:
TRIGONOMETRIC RELATIONS 
H = Hypotenuse 
A = Adjacent side 
O = Opposite side 
S = Sine 
C = Cosine 
T = Tangent 
q = angle between hypotenuse
and adjacent side (base)
f = angle
between hypotenuse and opposite side
LENGTH of SIDES for RIGHT  ANGLE TRIANGLES
Length of Hypotenuse = 
Side Opposite x Cosecant Side Opposite + Sine Side Adjacent x Secant Side Adjacent + Cosine 


Length of Side Opposite = 
Hypotenuse x Sine Hypotenuse + Cosecant Side Adjacent x Tangent Side Adjacent + Cotangent 


Length of Side Adjacent = 
Hypotenuse x Cosine Hypotenuse + Secant Side Opposite x Cotangent Side Opposite + Tang 
ANGLE FUNCTIONS 
SIGNS OF THE FUNCTIONS 
QUADRANT 
sinq 
cosq 
tanq 
I 
+ 
+ 
+ 
II 
+ 
 
 
III   
 
+ 
IV   
+ 
 
The
circular system of angular measurement is called radian measure.
A radian is an angle that intercepts an arc equal in length to the radius of a circle as
illustrated below.
Length of arc BC = radius of circle
6.28 radians = 360°
2p radians = 360°
p radians = 180°
1 radian = 57.2957795°
1 degree = 0.01745 radian
PYTHAGOREAN THEOREM 
In a right triangle, the square of the
hypotenuse is
equal to the sum of the squares of the other two sides.
c^{2} = a^{2} + b^{2}
a^{2} = c^{2}  b^{2}
b^{2} = c^{2}  a^{2}
^{ }
VARIOUS MEASUREMENTS 
Plane figures bounded by straight lines.
Area of a triangle whose base is (b) and altitude (h).
Area of a rectangle with sides (a) and (b).
area = ab
Area of a parallelogram with side (b) and
perpendicular distance to the parallel side (h).
area = bh
Plane figures bounded by curved lines.
Circumference of a circle whose radius is (r) and
diameter (d)
circumference = 2p r = p d
Area of a circle
area = p r^{2} = ¼p d^{2} = .7854d^{2}
Length of an arc of a circle for an arc of q degrees.
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