Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

TrigFunctions using SOHCAHTOA
SOH
...


TOA

Sine= opp/hyp
...
Tangent= opp/adj
SINE OF ANGLE = SINØ= OPP/HYP
IN order to find the sine of angle, you must know the lengths of the opposite side
& the hypotenus
...

Image

Note:
 the capital letters are the angles, wherever they are facing are the sides
denoted in small letters
...

Now looking for the sing
Using SOH CAH TOA
Since hyp= 14, and we are looking for sinf
SINF = OPP/ hyp, but opp= ?
Applying Pythagora's theorem to find 'f'=
opp
r2=f2+ k2 ( Pythagoras theorem)
14 2= f2 + 72
f2= 196 - 49
f2=147, f = √147, f = 7√49×3= 7√3
Since f= 7√3, now sinf=7 √3/14
Sinf f= √3/2

Page 1 of 4

COSINE OF ANGLE
COSØ= ADJ/HYP
EXAMPLE: A ladder leans against a
building, creating an Angle 75° with
the ground
...
Interpreting
question in the image below
Image 2:
Since adj= 3, length of the ladder = hyp= this makes it CAH
IN SOH CAH TOA
COSØ= 3/c, since the angle is given, ø=75°
Cos75 = 3/c, c=3/cos75
c = 11
...
6
TANGENT OF ANGLE
TANGENT= OPP/ADJ
EXAMPLE: An engineer working with a
39 foot tower with a wire attache to
the top of it
...
How far from the base of
the tower the wire should attach to the
ground
...
88

Page 2 of 4

RECIPROCAL OF TRIG FUNCTIN, ADDITIONAL TRIG FUNCTIONS: they are
the reciprocal of the normal trig functions
 Cosecant also written as cscø is the reciprocal of sine
...

Cot∅ = 1/ tan∅, since tan ∅ = opp/adj, Cot∅= adj/opp

INVERSE TRIG FUNCTIONS
The trig functions all have inverse, they are:
Arcsin= sin, arccos= cos, arctan= tan
In inverse trig function, ∅ (theta) is the unknown I
...

Inverse Trig
Inverse sin (arcsin) : ∅= sin-1 (opp/hypo)
Inverse cosine(arccos): ∅= sin-1(adj/hyp)
Inverse tangent (arctan): sin-1 (opp/adj)
Example: find angke ∅ in tan∅=1
...
7/ta (tan cancel out in the left hand side)
∅= tan-1 1
...
53

OBSERVATION/SUMMARY

Page 3 of 4






 The terms we are given and asked to find would determine if to
use SOH,CAH, TOA

---