Mission
People
Join Us
Pricing
FAQ
ibGuru - all in one IB study app
/
Subjects
/
Maths AA
/
Topics
/
3. Geometry and Trigonometry
ibGuru - all in one IB study app
/
Subjects
/
Maths AA
/
Topics
/
3. Geometry and Trigonometry
Share
Mission
People
Join Us
Pricing
FAQ
3. Geometry and Trigonometry
태그
Gallery view
Search
Sub-topics
Midpoint and distance:
To find the midpoint of two points
(
x
1
,
y
1
,
z
1
)
(x_1,y_1,z_1)
(
x
1
,
y
1
,
z
1
)
and
(
x
2
,
y
2
,
z
2
)
(x_2,y_2,z_2)
(
x
2
,
y
2
,
z
2
)
in three-dimensional space:
(
x
1
+
x
2
2
,
y
1
+
y
2
2
,
z
1
+
z
2
2
)
(\frac{x_1+x_2}2,\frac {y_1+y_2}2,\frac {z_1+z_2}2)
(
2
x
1
+
x
2
,
2
y
1
+
y
2
,
2
z
1
+
z
2
)
The distance
d
between two points
(
x
1
,
y
1
,
z
1
)
(x_1,y_1,z_ 1)
(
x
1
,
y
1
,
z
1
)
and
(
x
2
,
y
2
,
z
2
)
(x_2,y_2,z_2)
(
x
2
,
y
2
,
z
2
)
in three-dimensional space:
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
+
(
z
2
−
z
1
)
2
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
+
(
z
2
−
z
1
)
2
Circle geometry:
1.
Circumference
C
=
2
π
r
C=2\pi r
C
=
2
π
r
2.
Area
A
=
π
r
2
A=\pi r^2
A
=
π
r
2
3.
Length of arc
l
=
r
θ
l = r\theta
l
=
r
θ
4.
Area of sector
A
=
1
2
θ
r
2
=
1
2
r
l
A =\frac 12\theta r^2 =\frac 12rl
A
=
2
1
θ
r
2
=
2
1
r
l
5.
In a
polar
coordinate system we have:
x
=
r
cos
θ
x = r \cos\theta
x
=
r
cos
θ
and
y
=
r
sin
θ
y =r\sin\theta
y
=
r
sin
θ
.
3.1 Geometry
Applications
3.2 Trigonometry
Trigonometric functions are type of
periodic
functions where
f
(
x
+
T
)
=
f
(
x
)
f(x+T) = f(x)
f
(
x
+
T
)
=
f
(
x
)
for certain
T
T
T
.
There are three types of trigonometric functions you need to know:
sin
x
,
cos
x
,
tan
x
\sin x,\cos x,\tan x
sin
x
,
cos
x
,
tan
x
.
We now utilize a different measurement of angle, called
radian
, where
π
r
a
d
≡
180
˚
π rad ≡ 180˚
π
r
a
d
≡
180˚
.
r
a
d
i
a
n
=
d
e
g
r
e
e
⋅
π
180
radian=degree\cdot\frac{\pi}{180}
r
a
d
ian
=
d
e
g
ree
⋅
180
π
These are extremely useful in geometry, and in drawing functions.
3.3 Trig. Functions and Identities
3.4 Vectors (HL)
