Unit 2 - Objective 2 - Defining Trigonometric Functions


There are six possible ratios of two sides of a triangle.   These names are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).  Because these ratios depend on the size an angle Q, they are written sin Q, cos Q, tan Q, cot Q, sec Q, and csc Q.

u4obj201.gif (3462 bytes) r2 = x2 + y2

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Examples:

1.

Given the point (5, 12) on the terminal side of an angle Q, find the six trigonometric functions of Q.

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sin Q = y/r = 12/13
cos Q = x/r = 5/13
tan Q = y/x = 12/5
cot Q = x/y = 5/12
sec Q = r/x = 13/5
csc Q = r/y = 13/12

2.

Given the point (3,-5) on the terminal side of an angle Q, find the six trigonometric functions of Q.

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sin Q = -5/
cos Q = 3/
tan Q = -5/3
cot Q = -3/5
sec Q = /3
csc Q = -/5

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