Trionometry: RatioNirvana by: javier
Trionometry: Ratio Nirvana
by: javier
RR
RR The Goal & The Tools
The Goal & The Tools
□ Goal: to solve triangles
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret □ Tools: 30-60 Ratios
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret □ Tools: 30-60 Ratios □ Tools: 45-45 Ratios
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret □ Tools: 30-60 Ratios □ Tools: 45-45 Ratios □ Tools: almost-triangles ratios
The Ultimate Tool Knowing ALL the ratios
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios. 10o
Knowing ALL the ratios
We would like to know ALL the ratios. 11o
Knowing ALL the ratios
We would like to know ALL the ratios. 12o
Knowing ALL the ratios
We would like to know ALL the ratios.
13o
Knowing ALL the ratios
We would like to know ALL the ratios.
14o
Knowing ALL the ratios
We would like to know ALL the ratios.
15o
Knowing ALL the ratios
We would like to know ALL the ratios.
16o
Knowing ALL the ratios
We would like to know ALL the ratios.
17o
Knowing ALL the ratios
We would like to know ALL the ratios.
18o
Knowing ALL the ratios
We would like to know ALL the ratios.
19o
Knowing ALL the ratios
We would like to know ALL the ratios.
20o
Knowing ALL the ratios
We would like to know ALL the ratios.
21o
Knowing ALL the ratios
We would like to know ALL the ratios.
22o
Knowing ALL the ratios
We would like to know ALL the ratios.
23o
Knowing ALL the ratios
We would like to know ALL the ratios.
24o
Knowing ALL the ratios
We would like to know ALL the ratios.
25o
Knowing ALL the ratios
We would like to know ALL the ratios.
26o
Knowing ALL the ratios
We would like to know ALL the ratios.
27o
Knowing ALL the ratios
We would like to know ALL the ratios.
28o
Knowing ALL the ratios
We would like to know ALL the ratios.
29o
Knowing ALL the ratios
We would like to know ALL the ratios.
30o
Knowing ALL the ratios
We would like to know ALL the ratios.
31o
Knowing ALL the ratios
We would like to know ALL the ratios.
32o
Knowing ALL the ratios
We would like to know ALL the ratios.
33o
Knowing ALL the ratios
We would like to know ALL the ratios.
34o
Knowing ALL the ratios
We would like to know ALL the ratios.
35o
Knowing ALL the ratios
We would like to know ALL the ratios.
36o
Knowing ALL the ratios
We would like to know ALL the ratios.
37o
Knowing ALL the ratios
We would like to know ALL the ratios.
38o
Knowing ALL the ratios
We would like to know ALL the ratios.
39o
Knowing ALL the ratios
We would like to know ALL the ratios.
40o
Knowing ALL the ratios
We would like to know ALL the ratios.
41o
Knowing ALL the ratios
We would like to know ALL the ratios.
42o
Knowing ALL the ratios
We would like to know ALL the ratios.
43o
Knowing ALL the ratios
We would like to know ALL the ratios.
44o
Knowing ALL the ratios
We would like to know ALL the ratios.
45o
Knowing ALL the ratios
We would like to know ALL the ratios.
46o
Knowing ALL the ratios
We would like to know ALL the ratios.
47o
Knowing ALL the ratios
We would like to know ALL the ratios.
48o
Knowing ALL the ratios
We would like to know ALL the ratios.
49o
Knowing ALL the ratios
We would like to know ALL the ratios.
50o
Knowing ALL the ratios
We would like to know ALL the ratios.
51o
Knowing ALL the ratios
We would like to know ALL the ratios.
52o
Knowing ALL the ratios
We would like to know ALL the ratios.
53o
Knowing ALL the ratios
We would like to know ALL the ratios.
54o
Knowing ALL the ratios
We would like to know ALL the ratios.
55o
Knowing ALL the ratios
We would like to know ALL the ratios.
56o
Knowing ALL the ratios
We would like to know ALL the ratios.
57o
Knowing ALL the ratios
We would like to know ALL the ratios.
58o
Knowing ALL the ratios
We would like to know ALL the ratios.
59o
Knowing ALL the ratios
We would like to know ALL the ratios.
60o
Knowing ALL the ratios
We would like to know ALL the ratios.
61o
Knowing ALL the ratios
We would like to know ALL the ratios.
62o
Knowing ALL the ratios
We would like to know ALL the ratios.
63o
Ratio Nirvana: it’s a great day someone has put ratio buttons on the calculator
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
cos(θ) =
θ
adj hyp
tan(θ) =
opp adj
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
23o
cos(θ) =
adj hyp
tan(θ) =
opp adj
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
35o
cos(θ) =
adj hyp
tan(θ) =
opp adj
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
cos(θ) =
47o
adj hyp
tan(θ) =
opp adj
now backwards
now backwards if we know the ratio, we can find the angle
if we know the ratio, we can find the angle learn arccos(r), arcsin(r), arctan(r)
θ
if we know the ratio, we can find the angle
learn arccos(r), arcsin(r), arctan(r)
5 3 θ
if we know the ratio, we can find the angle
learn arccos(r), arcsin(r), arctan(r)
4 θ
3
if we know the ratio, we can find the angle learn arccos(r), arcsin(r), arctan(r)
5
θ
4
Mission Accomplished
Mission Accomplished start doing amazing
start doing amazing
□
start doing amazing
□
start doing amazing
□
by: javier
RR
RR The Goal & The Tools
The Goal & The Tools
□ Goal: to solve triangles
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret □ Tools: 30-60 Ratios
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret □ Tools: 30-60 Ratios □ Tools: 45-45 Ratios
The Goal & The Tools
□ Goal: to solve triangles □ Tools: Pythagorean Theorem □ Tools: The Secret □ Tools: 30-60 Ratios □ Tools: 45-45 Ratios □ Tools: almost-triangles ratios
The Ultimate Tool Knowing ALL the ratios
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios.
Knowing ALL the ratios
We would like to know ALL the ratios. 10o
Knowing ALL the ratios
We would like to know ALL the ratios. 11o
Knowing ALL the ratios
We would like to know ALL the ratios. 12o
Knowing ALL the ratios
We would like to know ALL the ratios.
13o
Knowing ALL the ratios
We would like to know ALL the ratios.
14o
Knowing ALL the ratios
We would like to know ALL the ratios.
15o
Knowing ALL the ratios
We would like to know ALL the ratios.
16o
Knowing ALL the ratios
We would like to know ALL the ratios.
17o
Knowing ALL the ratios
We would like to know ALL the ratios.
18o
Knowing ALL the ratios
We would like to know ALL the ratios.
19o
Knowing ALL the ratios
We would like to know ALL the ratios.
20o
Knowing ALL the ratios
We would like to know ALL the ratios.
21o
Knowing ALL the ratios
We would like to know ALL the ratios.
22o
Knowing ALL the ratios
We would like to know ALL the ratios.
23o
Knowing ALL the ratios
We would like to know ALL the ratios.
24o
Knowing ALL the ratios
We would like to know ALL the ratios.
25o
Knowing ALL the ratios
We would like to know ALL the ratios.
26o
Knowing ALL the ratios
We would like to know ALL the ratios.
27o
Knowing ALL the ratios
We would like to know ALL the ratios.
28o
Knowing ALL the ratios
We would like to know ALL the ratios.
29o
Knowing ALL the ratios
We would like to know ALL the ratios.
30o
Knowing ALL the ratios
We would like to know ALL the ratios.
31o
Knowing ALL the ratios
We would like to know ALL the ratios.
32o
Knowing ALL the ratios
We would like to know ALL the ratios.
33o
Knowing ALL the ratios
We would like to know ALL the ratios.
34o
Knowing ALL the ratios
We would like to know ALL the ratios.
35o
Knowing ALL the ratios
We would like to know ALL the ratios.
36o
Knowing ALL the ratios
We would like to know ALL the ratios.
37o
Knowing ALL the ratios
We would like to know ALL the ratios.
38o
Knowing ALL the ratios
We would like to know ALL the ratios.
39o
Knowing ALL the ratios
We would like to know ALL the ratios.
40o
Knowing ALL the ratios
We would like to know ALL the ratios.
41o
Knowing ALL the ratios
We would like to know ALL the ratios.
42o
Knowing ALL the ratios
We would like to know ALL the ratios.
43o
Knowing ALL the ratios
We would like to know ALL the ratios.
44o
Knowing ALL the ratios
We would like to know ALL the ratios.
45o
Knowing ALL the ratios
We would like to know ALL the ratios.
46o
Knowing ALL the ratios
We would like to know ALL the ratios.
47o
Knowing ALL the ratios
We would like to know ALL the ratios.
48o
Knowing ALL the ratios
We would like to know ALL the ratios.
49o
Knowing ALL the ratios
We would like to know ALL the ratios.
50o
Knowing ALL the ratios
We would like to know ALL the ratios.
51o
Knowing ALL the ratios
We would like to know ALL the ratios.
52o
Knowing ALL the ratios
We would like to know ALL the ratios.
53o
Knowing ALL the ratios
We would like to know ALL the ratios.
54o
Knowing ALL the ratios
We would like to know ALL the ratios.
55o
Knowing ALL the ratios
We would like to know ALL the ratios.
56o
Knowing ALL the ratios
We would like to know ALL the ratios.
57o
Knowing ALL the ratios
We would like to know ALL the ratios.
58o
Knowing ALL the ratios
We would like to know ALL the ratios.
59o
Knowing ALL the ratios
We would like to know ALL the ratios.
60o
Knowing ALL the ratios
We would like to know ALL the ratios.
61o
Knowing ALL the ratios
We would like to know ALL the ratios.
62o
Knowing ALL the ratios
We would like to know ALL the ratios.
63o
Ratio Nirvana: it’s a great day someone has put ratio buttons on the calculator
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
cos(θ) =
θ
adj hyp
tan(θ) =
opp adj
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
23o
cos(θ) =
adj hyp
tan(θ) =
opp adj
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
35o
cos(θ) =
adj hyp
tan(θ) =
opp adj
someone has put ratio buttons on the calculator SOH-CAH-TOA sin(θ) =
opp hyp
cos(θ) =
47o
adj hyp
tan(θ) =
opp adj
now backwards
now backwards if we know the ratio, we can find the angle
if we know the ratio, we can find the angle learn arccos(r), arcsin(r), arctan(r)
θ
if we know the ratio, we can find the angle
learn arccos(r), arcsin(r), arctan(r)
5 3 θ
if we know the ratio, we can find the angle
learn arccos(r), arcsin(r), arctan(r)
4 θ
3
if we know the ratio, we can find the angle learn arccos(r), arcsin(r), arctan(r)
5
θ
4
Mission Accomplished
Mission Accomplished start doing amazing
start doing amazing
□
start doing amazing
□
start doing amazing
□
