WARM-UP Write each function in terms of its cofunction. (a) cos 48° = sin (90° – 48°) = sin 42° (b) tan 67° = cot (90° – 67°) = cot 23° (c) sec 44° = csc (90° – 44°) = csc 46°

ID/Quadratic Quiz Write all identities Pythagoreans (3) Quotients (2) Cofunctions (6) Reciprocal (6) Solve the quadratics 5. x2 + 11x + 24 = 0 6. (x – 3)2 – 4 = 0 7. Write the quadratic formula.

Trig Game Plan Date: 9/24/13 2.1b Trig Functions of Acute Angles Section/Topic 2.1b Trig Functions of Acute Angles Objective (Trig Standard 9a) Students will be able to apply trig concepts to right triangles using right-triangle-based definitions and cofunctions ID’s. Homework (with announcements) p68 (23 to 42, 59 to 64) Late start tomorrow

Increasing/Decreasing Functions As A increases, y increases and x decreases. Since r is fixed, sin A increases csc A decreases cos A decreases sec A increases tan A increases cot A decreases

Determine whether each statement is true or false. Example 1a COMPARING FUNCTION VALUES OF ACUTE ANGLES Determine whether each statement is true or false. (a) sin 21° > sin 18° (b) cos 49° ≤ cos 56° (a) In the interval from 0 to 90, as the angle increases, so does the sine of the angle, which makes sin 21° > sin 18° a true statement. (b) In the interval from 0 to 90, as the angle increases, the cosine of the angle decreases, which makes cos 49° ≤ cos 56° a false statement.

Determine whether each statement is true or false. Example 1b COMPARING FUNCTION VALUES OF ACUTE ANGLES Determine whether each statement is true or false. (a) tan 25° < tan 23° In the interval from 0° to 90°, as the angle increases, the tangent of the angle increases. tan 25° < tan 23° is false. (b) csc 44° < csc 40° In the interval from 0° to 90°, as the angle increases, the sine of the angle increases, so the cosecant of the angle decreases. csc 44° < csc 40° is true.

30°- 60°- 90° Triangles Bisect one angle of an equilateral to create two 30°-60°-90° triangles.

30°- 60°- 90° Triangles Use the Pythagorean theorem to solve for x.

Find the six trigonometric function values for a 60° angle. Example 2 FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60° Find the six trigonometric function values for a 60° angle.

Find the six trigonometric function values for a 60° angle. Example 2 FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60° (continued) Find the six trigonometric function values for a 60° angle.

45°- 45° Right Triangles Use the Pythagorean theorem to solve for r.

45°- 45° Right Triangles adjacent

45°- 45° Right Triangles

Function Values of Special Angles  sin  cos  tan  cot  sec  csc  30 45 60