(altitude to the hypotenuse)2 =
(one piece of the hypotenuse) · (other piece of the hypot.)
(leg)2 =
(whole hypotenuse) · (piece of hypotenuse closest to leg)
B
e
D
c
a
f
g
C
C
A
b
B
a
b
e
g
D
D
f
A
g
C
SOHCAHTOA
sin θ
cos θ
tan θ
sin(angle) = ratio
Sin-1(ratio) = angle
If sin A = k, then Sin-1(k) = A
example: sin 30° = ½, Sin-1(½) = 30°
If cos A = k, then Cos-1(k) = A
example: cos 60° = ½, Cos-1(½) = 60°
If tan A = k, then Tan-1(k) = A
example: tan 45° = 1, Tan-1(1) = 45°
Use trig. buttons (sin, cos, tan) for finding ratios if you know the angles.
Use inverse trig. buttons (sin -1, cos-1, tan-1) for finding angles if you know
the ratios.
Angles of Elevation and Depression
are both taken off of horizontal lines
angle of depression from A to B
A
B
angle of elevation for B to A
Percentage Grade refers to vertical change compared to horizontal
change. Example: 6% grade means the line is going up 6 units for
every 100 units it is going over.
A vector has both magnitude and direction.
Magnitude is the length or speed of the vector.
Direction is the angle measure off of horizontal.
Component form is the <x, y> form
that describes the movement from
the initial point to the terminal point.
Equal vectors - vectors having same magnitude
and same direction
Parallel vectors - Vectors having the same or
opposite directions
Resultant vector - a vector that represents the
sum of two given vectors