Trigonometry - physicsphenomena

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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  b^2 = c^2 - a^2 Relationship among the lengths of sides.

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 A c b a

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 = hyp * Sin 30 degrees opp = 10 m * Sin 30 deg Opp = 5.0 m Adj = 8.66 m Cos 30 degrees = adj / hyp Adj = hyp * cos 30 degrees Adj = 10 m * Cos 30 deg Hyp 10 m 30 degrees

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 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 A b a B 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