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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 1. Pythagoreans (3) 2. Quotients (2) 3. Cofunctions (6) 4. Reciprocal (6) Solve the quadratics 5. x2 + 11x + 24 = 0 6. (x – 3)2 – 4 = 0 7. Write the quadratic formula. Trig Game Plan Section/Topic Objective (Trig Standard 9a) Date: 9/24/13 2.1b Trig Functions of Acute Angles Students will be able to apply trig concepts to right triangles using right-triangle-based definitions and cofunctions ID’s. Homework (with p68 (23 to 42, 59 to 64) announcements) 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 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. 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. Example 2 FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60° 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 30 45 60 sin cos tan cot sec csc