s o h - c a h - t o a j 1 - weebly
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Trigonometry Notes
TRIGONOMETRY: TRIGONOMETRIC RATIO:
S O H - C A H - T O A
* ϴ = any acute angle in a right triangle
Example 1 Express each ratio as a fraction in simplest form and as a decimal to the nearest hundredth a) Sin P d) Cos P b) Tan P e) Sin Q c) Cos Q f) Tan Q
SOH-CAH-TOA
Sine
Cosine
Tangent
A
B C a
c
R
Q
15
17
thestudy oftrigonometrytriangle Tsmeasure involvestrianglemeasure
Aratioofthelengthsoftwosidesof arighttriangle theyare constantfor a
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Eine f Hypotenuse JAdjacent 1 tangent 1 Adjacent
IppositeIpposite Eosine Hypotenuse
sin opposite sina.az SinB behypotenuse
cos Adjacent cosA b CosB ahypotenuse c C
tan opposite Tana a tanB badjacent b a
gC
g YF 0.88 f 0.47I
1.88 8 20.4717
1,4 0.88 185 0.53
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Example 2 Find each ratio as a fraction in simplest form and as a decimal to the nearest hundredth a) sin J b) cos J c) tan J d) sin K e) cos K f) tan K Example 3 Example 4 Find x to the nearest hundredth Find x to the nearest hundredth
InverSe TrIg rATIOS
x Inverse sine x Inverse cosine x Inverse tangent
K
J L
13 5
12
SOH CAH TOA
5,3 0.38 92
72 041 1,13 0.925 38 3 2.413
Scott CAH
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used to find themeasure of a missing anglein a right triangle youneed a calculator
If SinA X then sin x MLA
tf CosA X then cos X mcA
Atan A x then tan x MCA
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Examples Use a calculator to find m∠A to the nearest tenth 1. 2. 3. 4.
A B tanA
fors ynA 9 A tan fo27 6
A sin Ya cC A
r 02nd 182720
B 8 CmcA ymA
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r tan A 9cosA C B S
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IF l
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Rme F 25 22.6 sin F I mop 570mega 670674 13
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SOLVING RIGHT TRIANGLES
whengivenI I 1
Special Right 1 SIDE AND
Triangle 1 ANGLE 2 SIDESl I I r r
usetrig ratios Find a Find a4590 30 6090 soft CAH Toa solve missingside missingangle
4 J forthemissing side 1Labelside Labelside I Pythagorean InverseTngratios ratios soy CAH Theorem Ratios
ninink thinkingn ops cos adj a'tb2c2a SOHCAHTO
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7hrs30 Inverse sine inventeCosineLatin gopwwegf.gr Toa Asintoff mcAosyad
slugin tanX oppadj InverseTangent
mcAtanyodr.gr
use triangle sum theorem tofind missing angle All Ls addupto
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