H.Melikian/1200 5.3 Trigonometric Functions of Any Angles. The Unit Circle Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ [email protected]1. Use the definitions of trigonometric functions of any angle. 2. Use the signs of the trigonometric functions. 3. Find reference angles. 4. Use reference angles to evaluate trigonometric functions.
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H.Melikian/12001 5.3 Trigonometric Functions of Any Angles. The Unit Circle Dr.Hayk Melikyan/ Departmen of Mathematics and CS/ [email protected] 1. Use.
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H.Melikian/1200 1
5.3 Trigonometric Functions of Any Angles.The Unit Circle
Dr .Hayk Melikyan/ Departmen of Mathematics and CS/ [email protected]
1. Use the definitions of trigonometric functions of any angle.2. Use the signs of the trigonometric functions.3. Find reference angles.4. Use reference angles to evaluate trigonometric functions.
H.Melikian/1200 2
Definitions of Trigonometric Functions of Any Angle
Let be any angle in standard position and let P = (x, y) be a point on the terminal side of If is the distance from (0, 0) to (x, y), the six trigonometric functions of are defined by the following ratios:
2 2r x y
sinyr
cosxr
tan , 0yx
x
csc , 0ry
y
sec , 0rx
x
cot , 0xy
y
H.Melikian/1200 3
Example: Evaluating Trigonometric Functions
Let P = (1, –3) be a point on the terminal side of Find each of the six trigonometric functions of P = (1, –3) is a point on the terminal side of x = 1 and y = –3