Although the results of Arts. 12, 15, 16, 17 have been proved from diagrams where A is less than a right angle, the Bisect it by the straight line OB, so that ZAOB = and draw CD perpendicular to OA, meeting OB in E. (3.) A 2(1 - sin2 4)-1=1-2 sin3 — (4.) 19. To find the trigonometrical ratios of 15°, 75°, 120°, 135°, 150°. We have, sin 75° = sin (90° 15°) = cos 15° = √√3+ 1 2√2 = (5.) Ratios of 135°. = tan (90° — 15°) = cot 15° We have, sin 135° sin (180°- 135°) = sin 45° : = = = tan 45° 1. Define a negative angle, and show that tan (-A) tan A, when A lies between – 90° and – 180°. 2. Trace the changes of sign of sin A. cos A through the four quadrants. 3. Trace the changes of sign of cos A + sin A, and of cos A - sin A, as A changes from 45° to 315°. |