Introduction to College Algebra & Trigonometry Algebra and Trigonometry Chapter 6 – Trigonometry Section 6.3 – Trigonometric Functions of Any Angle

Section 6.3 – Trigonometric Functions of Any Angle Let be an angle in standard position with (x, y) a point on the terminal side of and r y x

Section 6.3 – Trigonometric Functions of Any Angle Example: (-5,12) 13 12 -5

Section 6.3 – Trigonometric Functions of Any Angle You try: Determine the exact values of the six trigonometric functions of the angle in standard position whose terminal side contains the point (-3, -7).

Section 6.3 – Trigonometric Functions of Any Angle Signs of Trig Functions Quadrant II Quadrant I S A T C Quadrant III Quadrant IV

Section 6.3 – Trigonometric Functions of Any Angle You try:

Section 6.3 – Trigonometric Functions of Any Angle Reference angles – the acute angle formed by the terminal ray and the x-axis.

Section 6.3 – Trigonometric Functions of Any Angle You try: Find the reference angle for

Section 6.3 – Trigonometric Functions of Any Angle Evaluating Trig. Functions of Any Angle To find the value of a trig. Function of any angle, Determine the function value for the associated reference angle; Depending on the quadrant in which the original angle lies, affix the appropriate sign to the function value.

Section 6.3 – Trigonometric Functions of Any Angle You try: Evaluate

Section 6.3 – Trigonometric Functions of Any Angle You try: Find two values of that satisfy the equation Do not use you calculator.

Section 6.3 – Trigonometric Functions of Any Angle Using a calculator to solve or evaluate trig functions To evaluate csc, sec & cot using the calculator, use the appropriate reciprocal function.

Section 6.3 – Trigonometric Functions of Any Angle Using a calculator to solve or evaluate trig functions To solve for the missing angle, use the inverse trig function keys.

Section 6.3 – Trigonometric Functions of Any Angle You try: Solve the equation for

Section 6.3 – Trigonometric Functions of Any Angle You try: Solve the equation for

Section 6.3 – Trigonometric Functions of Any Angle You try: Solve the equation for

Section 6.3 – Trigonometric Functions of Any Angle Definition of a Periodic Function A function f is periodic if there exists a positive real number p such that for all x in the domain of f. The smallest number p for which f is periodic is called the period of f.

Section 6.3 – Trigonometric Functions of Any Angle Even and Odd Trigonometric Functions The cosine and secant functions are even. The sine, cosecant, tangent, and cotangent functions are odd.