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Chapter 6

# Chapter 6 - Chapter6: (6.1 Vocabulary:.The < = angel = = <...

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Chapter 6: Trigonometric Functions of Angels Trigonometric Functions of Acute Angels (6.1) Vocabulary: An angel is a figure formed by two rays with a common end point. The common end point is called the vertex. < = angel = θ = < ABC One measurement of angel is degrees. A full rotation is 360 degrees. The degree is sub‐divided into smaller units. The minute (1/60 th of a degree) and second (1/60 th of a minute) Acute angels have measure 0 0 < θ < 90 0 Ex: Obtuse angels have measure 90 0 < θ < 180 0 Ex:

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Definition: Let θ be an acute angel placed in a right triangle. The basic trig functions are defines as follows: You can remember the definition of the basic trigonometric functions by remembering SOHCAHTOA Reciprocal Identities can be defined from the basic trig functions as follows: Ex: Δ ABC is a right triangle with AC = 3, BC = 2 and <C = 90 0 Find the six trigonometric functions:
Calculate sin (25 0 ) , cos (25 0 ) and tan (25 0 ) using degree mode in your calculator. Two well known triangles from Geometry: 30 0 ‐60 0 Right Triangle Theorem: In a 30 0 ‐60 0 right triangle, the length of the opposite side to the 30 0 angel is half of the length of the hypotenuse. 45 0 ‐45 0 Right Triangle Theorem: In a 45 0 ‐45 0 right triangle, the length of the opposite and the adjacent sides are equal.

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Let’s now make a table with the trig functions with all the special angels where you can express them as an exact answer (without calculator). You have to memorize this table asap. Prove: cos(60 0 ) = cos 2 (30 0 ) – sin 2 (30 0 )
Algebra and the Trigonometric Functions (6.2) Notation: 1) sin( θ ) = said assin e of the angel θ = sin θ In this case θ is the input and sin θ is the output Note: sin θ is a value ; For example, sin(30 0 ) = ½ 2) When you are multiplying with two trigonometric quantities, parenthesis is often omitted. For example, (sin θ )(cos θ ) = sin θ cos θ Similarly (sin θ )(sin θ ) = sin 2 θ (sin θ ) n = sin n θ (n -1) The convention stated above applies to the other five trig functions.

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Chapter 6 - Chapter6: (6.1 Vocabulary:.The < = angel = = <...

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