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Section 5.2 Trigonometric Function of Real Numbers

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## Section 5.2 Trigonometric Function of Real Numbers

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**Chapter 5 – Trigonometric Functions: Unit Circle Approach**Section 5.2 Trigonometric Function of Real Numbers 5.2 - Trigonometric Function of Real Numbers**Definition of the Trig Functions**5.2 - Trigonometric Function of Real Numbers**Example – pg. 384**• Find sin t and cost for the values of t whose terminal points are shown on the unit circle in the figure. t increases in increments of /4. 5.2 - Trigonometric Function of Real Numbers**Special Values**5.2 - Trigonometric Function of Real Numbers**Domains of the Trig Functions**Function Domain sin, cos All real numbers tan, sec All real numbers other than for any integer n cot, csc All real numbers other than n for any integer n 5.2 - Trigonometric Function of Real Numbers**Signs of the Trig Functions**Quad Positive Functions Negative Functions I All None II sin, csccos, sec, tan, cot III tan, cot sin, csc, cos, sec IV cos, sec sin, csc, tan, cot 5.2 - Trigonometric Function of Real Numbers**Example – pg. 384**• Find the exact value of the trigonometric functions at the given real number. 5.2 - 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. 5.2 - Trigonometric Function of Real Numbers**Even-Odd Properties**• Sine, cosecant, tangent, and cotangent are odd functions. • Cosine and secant are even functions. 5.2 - Trigonometric Function of Real Numbers**Example – pg. 384**• Find the exact value of the trigonometric functions at the given real number. 5.2 - Trigonometric Function of Real Numbers**Fundamental Identities**• Reciprocal Identities • Pythagorean Identities 5.2 - 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. 5.2 - Trigonometric Function of Real Numbers**Examples – pg. 385**• Find the values of the trigonometric functions of t from the given information. 5.2 - Trigonometric Function of Real Numbers**Examples – pg. 384**• Find the exact value of the trigonometric functions at the given real number. 5.2 - Trigonometric Function of Real Numbers