Section. Rigt Triangle Trigonometr. Reflection in te -ais and a vertical sift two units upward =. f Reflection in te -ais and a orizontal sift tree units to te left = ( + ) = = Section. Rigt Triangle Trigonometr You sould know te rigt triangle definition of trigonometric functions. (d) (e) (f) You sould know te following identities. (d) (e) (f) (g) () (i) (j) (k) and 90, You sould know tat two acute angles are complementar if and tat te cofunctions of complementar angles are equal. You sould know te trigonometric function values of 0,, and 0, or be able to construct triangles from wic ou can determine tem. Hpotenuse Adjacent side Opposite side Vocabular Ceck otenuse. (i) (e). osite; acent; otenuse acent acent (ii) (f). elevation; depression osite (iii) (iv) (v) (vi) otenuse osite acent otenuse osite otenuse osite acent (d)
Capter Trigonometr. 8 00 0 8 0 8 0 8 0 0 8 8. 9 b. 9 8 8 00 0 9 9 0 9 0 9 0 0 9.. 8 Te function values are te same ce te triangles are similar and te corresponding sides are proportional.
Section. Rigt Triangle Trigonometr. 8 7. 7. 7 8 89 7 8 7 7 8 7 8 7 8 7 8 7 7. 7 7 7. 8 7 7 7. 7. 8 7 8 7 Te function values are te same because te triangles are similar, and corresponding sides are proportional. 7.. 0.7.. 0.7. 0.7. 0.7. 0.7 Te function values are te same ce te triangles are similar and te corresponding sides are proportional. 8. Te function values are te same because te triangles are similar, and corresponding sides are proportional.
Capter Trigonometr 9. Given: 7 7 7 7 7 7 7 7 0. 7 7 7 7 7 7. Given:.. Given: 0 0 0 0 0 0 0 0.
Section. Rigt Triangle Trigonometr. Given:. 7 7 7 7 7 7 7 77 7 7 7 7 7 7 7 7. 0 0 0 0 80 radian 0 8. degree radian value 9. 80 0 0. degree radian value. 0 0 0 radian. degree radian value. 80 0. degree radian value. 80. degree radian value 0 0 0 0
Capter Trigonometr 7. 0, 0 0 0 0 0 0 (d) 0 0 0 0 0 8. 0, 0 0 0 0 90 0 0 0 0 0 (d) 0 0 9., (d) 90 0., 90º (d).. 8 9 90º (d) (d) 90....
Section. Rigt Triangle Trigonometr 7 7. 8. 9. 0..... 0.8. 0.8... 0.8.... 8 8 0 0.998 7 7 0 0.909...99. 87. 8 0 7 7. Make sure tat our calculator is in radian mode..07 0.989 8. 0.7 (Note: 0.7 is in radians) 0.7 0.77.7 0.7 9. Make sure tat our calculator is in radian mode..88 0. 0..88 0.. 0 0. º
8 Capter Trigonometr. 0. 0 0. 0. 0 7. 0 0 0 0 0 0 8. 0 8 8 0 8 9 9. 0 0 0. 0 r r 0 0 0. 8. 8 Heigt of te building: 8. meters 70 feet 8 m Disce between friends: 8 8. meters Not drawn to scale. 000 ft 00 ft 00 000 0. w 00 w 00 7. feet
Section. Rigt Triangle Trigonometr 9. 0 0 8.9 feet 0 0. feet Moving down te line: Dring verticall: 0 0.98 feet per ond feet per ond ft. Let te eigt of te mountain. 7. Let te orizontal disce from were te 9 angle of elevation is sigted to te point at tat level directl below te mountain peak. Ten. and 9. 9 Substitute 9 9 into te epression for... 9.. 9. 9 9. 9. 9. 9..9 Te mountain is about. miles ig. 9 9 0 0 0 0 8 0 0 8, 8, 8 (, ) (, ) 0 0 8 0 0 8, 8, 8
0 Capter Trigonometr 8. d.7 centimeters 9. 0 (e) Angle, Heigt (in meters) 80 9.7 70 8.8 (f) Te eigt of te balloon decreases. 8 8 0 0 7. 0. 0.9 0 0 8 9.9 meters (d) Te side of te triangle labeled will become sorter. 0 0.0 0.8 0. 70. 9.97,.0 0 0. 0 0 0.9 0 0 0. 0.7 0 0.0 0 0.9 7. 0 0 True, 0 0 0 0 7. True, because 90.7. False, 7. True, because. 7. 0 0 False, 0 0 0.7 0 0 0.09
Section. Rigt Triangle Trigonometr 7. 0.8 0.8 False. 0.8 0. 0.7 0.8 0.8.00 77. Tis is true because te corresponding sides of similar triangles are proportional. 78. Yes. Given, can be found from te identit. 79. In te interval 0, 0., 0. 0. 0. 0. 0. 0.0998 0.987 0.9 0.89 0.79 As 0, 0, >. and. 80. 0 0. 0. 0.9.. 0 0.9 0. 0.78 0.90 0.997 0.9 0.8 0. 0. 0.0707 On 0,., is an increag function. On 0,., is a decreag function. (d) As te angle increases te lengt of te side osite te angle increases relative to te lengt of te otenuse and te lengt of te side acent to te angle decreases relative to te lengt of te otenuse. Tus te e increases and te ine decreases. 8., ± 8. t t 9 t t t t 9 t t t t 9 9 t t t t t t t t t t t t t t, t ±, 8. 0 0 0 8., 0,