Chapter 5 – Trigonometric Functions: Unit Circle Approach 5.2 - Trigonometric Function of Real Numbers.

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Presentation transcript:

Chapter 5 – Trigonometric Functions: Unit Circle Approach Trigonometric Function of Real Numbers

Definition of the Trig Functions Trigonometric Function of Real Numbers

Example – pg. 384 Find sin t and cos t for the values of t whose terminal points are shown on the unit circle in the figure. t increases in increments of  / Trigonometric Function of Real Numbers

Special Values Trigonometric Function of Real Numbers

Domains of the Trig Functions FunctionDomain sin, cosAll real numbers tan, secAll real numbers other than for any integer n cot, cscAll real numbers other than n  for any integer n Trigonometric Function of Real Numbers

Signs of the Trig Functions QuadPositive Functions Negative Functions I All None II sin, csccos, sec, tan, cot III tan, cotsin, csc, cos, sec IV cos, secsin, csc, tan, cot Trigonometric Function of Real Numbers

Example – pg. 384 Find the exact value of the trigonometric functions at the given real number Trigonometric Function of Real Numbers

Examples – pg. 385 Find the sign of the expression if the terminal point determined by t is in the given quadrant Trigonometric Function of Real Numbers

Even-Odd Properties Sine, cosecant, tangent, and cotangent are odd functions. Cosine and secant are even functions Trigonometric Function of Real Numbers

Example – pg. 384 Find the exact value of the trigonometric functions at the given real number Trigonometric Function of Real Numbers

Fundamental Identities Reciprocal Identities Pythagorean Identities Trigonometric Function of Real Numbers

Examples – pg. 385 Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant Trigonometric Function of Real Numbers

Examples – pg. 385 Find the values of the trigonometric functions of t from the given information Trigonometric Function of Real Numbers

Examples – pg. 384 Find the exact value of the trigonometric functions at the given real number Trigonometric Function of Real Numbers