TRIGONOMETRY AND GEOMETRY

Remember:

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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

 

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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

-

+

-

RADIAN MEASURE

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
.

c2 = a2 + b2

a2 = c2 - b2

b2 = c2 - a2


VARIOUS MEASUREMENTS

Plane figures bounded by straight lines.


Area of a triangle whose base is (b) and altitude (h).

 

 

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Area of a rectangle with sides (a) and (b).

area = ab

 

 

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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 r2 = p d2 = .7854d2

Length of an arc of a circle for an arc of q degrees.

 

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