How do we draw angles in standard position? Angles of Rotation Essential Questions How do we draw angles in standard position? How do we determine the values of the trigonometric functions for an angle in standard position? Holt McDougal Algebra 2 Holt Algebra 2

For an angle θ in standard position, the reference angle is the positive acute angle formed by the terminal side of θ and the x-axis. Later, you will learn how to use reference angles to find trigonometric values of angles measuring greater than 90° or less than 0°.

Finding Reference Angles Find the measure of the reference angle for each given angle. 1.  = 135° 2.  = –105° –105° The measure of the reference angle is 45°. The measure of the reference angle is 75°.

Finding Reference Angles Find the measure of the reference angle for each given angle. 3.  = 325° 4.  = –115° –115° The measure of the reference angle is 35°. The measure of the reference angle is 65°.

Finding Reference Angles Find the measure of the reference angle for each given angle. 5.  = 310° 6.  = 105° 310° 105° The measure of the reference angle is 50°. The measure of the reference angle is 75°.

To determine the value of the trigonometric functions for an angle θ in standard position, begin by selecting a point P with coordinates (x, y) on the terminal side of the angle. The distance r from point P to the origin is given by .

Finding Values of Trigonometric Functions Using a point on the terminal side of  in standard position, find the exact value of the six trigonometric functions for θ. 7. P (–6, 9)

Finding Values of Trigonometric Functions Using a point on the terminal side of  in standard position, find the exact value of the six trigonometric functions for θ. 8. P (–3, 6)

Finding Values of Trigonometric Functions Using a point on the terminal side of  in standard position, find the exact value of the six trigonometric functions for θ. 9. P (–15, –8)

Lesson 10.2 Practice B