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TRIGONOMETRY

TRIGONOMETRY. . Sign for sin  , cos  and tan . Quadrant II 90 ° <  < 180°. SIN  (+). ALL (+). Quadrant I 0 ° <  < 90°.  = 180 °− . Let  = acute angle.  = . . . . .  = 180 °+ .  = 360 °− . TAN  (+). COS  (+). Quadrant IV 270 ° <  < 360°.

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TRIGONOMETRY

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  1. TRIGONOMETRY

  2. Sign for sin , cos  and tan  Quadrant II 90° <  < 180° SIN  (+) ALL (+) Quadrant I 0° <  < 90°  = 180°−  Let  = acute angle  =       = 180°+   = 360°−  TAN  (+) COS  (+) Quadrant IV 270° <  < 360° Quadrant III 180° <  < 270°

  3. Finding angle  when given sin  Quadrant I 0° <  < 90°  =  Quad I & Quad II sign (+) Given that 0°   360°, find  when sin  = 0.7660 sin  = −0.5736 • = sin-1 0.7660 • = 50° (acute angle)   = 50°, 130° Quadrant II 90° <  < 180° SIN  (+)  = 180°−  Quad III & Quad IV sign (−) Quadrant III 180° <  < 270° • = sin-1 0.5736 • = 35°   = 180° + 35°, 360°−35° = 215°, 325° TAN  (+)  = 180°+  Quadrant IV 270° <  < 360° COS  (+)  = 360°− 

  4. Finding angle  when given cos  Quadrant I 0° <  < 90°  =  Quad I & Quad IV sign(+) Given that 0°   360°, find  when • cos  = 0.7660 • cos  = −0.5736 • = cos-1 0.7660 • = 40°   = 40°, 360 − 40° = 40°, 320° Quadrant 2 90° <  < 180° SIN  (+)  = 180°−  Quadrant 3 180° <  < 270° Quad II & Quad III sign (−) TAN  (+) • = cos-1 0.5736 • = 55°   = 180° −55°, 180°+35° = 125°, 235°  = 180°+  Quadrant 4 270° <  < 360° COS  (+)  = 360°− 

  5. Find angle  when given tan  Quadrant 1 0° <  < 90°  =  Quadrant I and Quadrant 3 sign (+) Given that 0°   360°, find  when • tan  = 1.7660 • tan  = −2.5 • = tan-1 1.7660 • = 60°29’ Hence  = 60°29’, 180° + 60°29’ = 60°29’, 240° 29’ Quadrant 2 90° <  < 180° SIN  (+)  = 180°−  Quadrant 2 and Quadrant 4 Quadrant 3 180° <  < 270° sign (−) TAN  (+) • = tan-1 2.5 • = 68°12’ Hence  = 180° − 68°12’, 360°−68°12’ = 111°48’, 291°48’  = 180°+  Quadrant 4 270° <  < 360° KOS  (+)  = 360°− 

  6. Practice makes perfect!!! 1. Given sin x° =0.7547 and 90° x  180°, find x. 2. Given cos x = cos 34° and 270° x  360°, find x. 3. Given cos x = − 0.6926 and 90° x 180°, find x. 4. Given tan x = 0.8 and 180° x  360°, find x. 5. Given tan x = −0.8098 and 270° x  360°, find x. Answer: (1) 131° (2)326° (3)133°50’ (4)218°40’ (5)321°

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