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Trigonometry, sin Cah toa, right triangles 

https://content-eu-central-1.knowunity.com/CONTENT/afphIPGsTEkkfUPzONys_COMPRESSED.pdf

trig_ch_6

Study note

Ashley Ngokwere

United States of America

DEFAULT

Pre-Calculus

Polar coordinates

Complex numbers

Polar form of complex numbers

12/₁1
TUE 6.3 (part 2) Polar Coordinates.
Rectangular
(x, y)
x=rcos8
or
r 0
ex 1) Convert to rect. coords.: (3, πT)
SOHCAH TOA
X
Polar x² + y² = √²
x=rcoso
(r, 0)
=
з соз П
= 3.(-1)=-3
ex 2) Convert to rect. coords.
= 3(0)=0
(-10,7)
x=rcoso
y = rsind
=-10 sin
= 10 cos
=-10 (12) = -5√3 = 40 ( 2 ) = -5
ex 3) Convert to polar coords:y (1₁-√3)
x
tan 0 ==
x² + y² = √²
(1) ²³²+ -√3)² = √²
1+3_=r²
2=r
y=rsing
=3sin
→quadrantal 4
or ... x² + y² = 1² & tan 9 = 2/
~(blah)
X
tanh và
10 = tan = ²^(-√3)
*0
*ex 4) Convert to polar coords: (-2,2)
Special A.
² + y² = √²² & tan 9 = 2/
・(blah)
= 60°
ref 4
::
::
0
*
ex 5) Convert to polar coords: (0,-4)
::(4,3)
y = rsing
tang= y
(0,0²
jx
q
(0,₁)
(૯૧,૦)
(-3,0)
х,у
Qut
QN
(2√2, &T) T
(2, TT)
13/T
34
Sta
√3
Ford
(-5√3, -5)
x
(1,0)
5
2√2
*²
24
• (9-4) Equations
Tine
ex 6) Convert to polar: 5x-y=6
:
Rect →→→→ Polar
Isolater
5 (rcoso) - (rsind) = 6
5rcoso - rsind = 6
r (56ose - sind) = 6
6
r=
5 coso-sind
ex 7) Convert to Polar :
Circle → x² + (y + 1)² = 1
2
subst
r²+2rsind=
r(r + 2 sind) = 0
Xe
dy x² + y² = r²
x=rcoso
y=rsing
2
(rcoso)² + (rsin 0+1 ) ²³ = 1
r²cos²0 + (rsme + ₁)(rsing +() = 1
* r² cos²0 + r² sin²0 +2rsind +X=X
r ² (cos²0 + sin²8) + 2rsin = 0
factor.
= 0
subst
isolate r
substr²_4² Square both sides.
(x² + y² = 16
product of factors
or r+2sing =0
(r=-2sm
ex 8) Convert to Rect.: exa) Convert to Rect.:
r=4
0:34
tan both
FOIL
Subst
tan O= tan 31 QI
tano = -1
५
*
x.
tand= y
x
5x-bzy
= -1.x
y=-x
Sdes.... ex 10) Convert to Rectangular
r= -2 seco
-2
coso
⋅rcos 0= -2
x = -2
costr=
subst
.
Cos
Mult both
sides
HW p 673, #34-74 even

Polar coordinates

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Polar coordinates

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying