Transcript Trigonometry - physicsphenomena

Trigonometry
Review of Pythagorean Theorem
Sine, Cosine, & Tangent Functions
Laws of Cosines & Sines
Pythagorean Theorem
 c^2 = a^2 + b^2
 a^2 = c^2 - b^2
Relationship among the
lengths of sides.
 b^2 = c^2 - a^2
Side a
Side c
Side b
Right triangles in Trigonometry
 The letters a, b, and c are lengths of sides.
 The Letter A is the measure of an angle.
A Right Triangle
c
A
a
b
Trig functions and the right /\
 Sine (A) = opposite side / Hypotenuse
 Cosine (A) = adjacent side / Hypotenuse
 Tangent (A) = opposite side / adjacent side
Trig function values are the
ratios of the lengths of sides.
Sin A = Side a / Side c
Cos A = Side b / Side c
Tan A = Side a / Side b
c
a
A
b
Trig. Questions:
 What is the sine of 30 degrees?
 Written Sin 30, its _____.
 What is the Cosine of 30 degrees?
 Written Cos 30, its _____.
 What is the tangent of 30 degrees?
 Written Tan 30, its _____.
 Note: An angle may be also expressed in
radians; Set your calculator correctly.
More Trig Questions
 What is the Inverse Sin (0.5000)?
 Use 2nd function key for Inverse.
 What is the Inverse Cos (0.8660)?
 Use 2nd function key for Inverse.
 What is the Inverse Tan (0.5774)?
 Use 2nd function key for Inverse.
How to remember the functions
 Word Play
Sine Function: SOH
Cosine Function: CAH
Tangent Function: TOA
Thus: SOH CAH TOA
An example Trig problem:
 Imagine a right triangle having an angle of
30 degrees. The other non-right angle would
be 60 degrees. The 30 degree and the 60
degree angles would be called
complementary angles. Let the hypotenuse
equal 10 m. Calculate the length of the
opposite and adjacent sides.
 Well how are you going to do it?
Calculating the hypotenuse.
Sin 30 degrees = opp / hyp
Opp = 5.0 m
Opp = hyp * Sin 30 degrees
Adj = 8.66 m
opp = 10 m * Sin 30 deg
Cos 30 degrees = adj / hyp
Hyp
Adj = hyp * cos 30 degrees
Adj = 10 m * Cos 30 deg
30 degrees
10 m
Trigonometry Tables
 Many people have figured out the right
angle trig function values and published
them in table form. Often these tables can
be seen in the backs of trigonometry
textbooks, physics textbooks, and
engineering textbooks. Calculators now
have these function built on to them too.
 Go To www.google.com and look for
trigonometry tables or check a textbook.
Law of Cosines:
 Says: c^2 = a^2 + b^2 - 2 a b Cos C
 A, B, and C are interior angles
 and a, b, c are the lengths of the sides that
are opposite each angle respectively.
C
b
a
B
A
c
Law of Sines
 Says: a / Sin A = b / sin B = c / sin C
 Where A, B, and C are interior angles
 and a, b, c are lengths of sides.
A
b
c
C
B
a