TRIGONOMETRY Sign for sin cos and tan Quadrant

TRIGONOMETRY

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

Quadrant I 0° < < 90° = Quadrant II 90° < < 180° SIN (+) Finding angle when given sin Given that 0° 360°, find when Quad I sign (+) sin = 0. 7660 & Quad II a= 0. 7660 a = 50° (acute angle) = 50°, 130° sin-1 = 180°− Quadrant III 180° < < 270° TAN (+) = 180°+ Quadrant IV 270° < < 360° COS (+) = 360°− sin = − 0. 5736 sign (−) a= sin-1 0. 5736 a = 35° = 180° + 35°, 360°− 35° = 215°, 325° Quad III & Quad IV

Quadrant I 0° < < 90° = Finding angle when given cos Given that 0° 360°, find when Quad I sign(+) (a) cos = 0. 7660 & Quadrant 2 90° < < 180° SIN (+) = 180°− Quadrant 3 180° < < 270° TAN (+) = 180°+ Quadrant 4 270° < < 360° COS (+) = 360°− Quad IV a= cos-1 0. 7660 a = 40°, 360 − 40° = 40°, 320° (b) cos = − 0. 5736 sign (−) a= cos-1 0. 5736 a = 55° = 180° − 55°, 180°+35° = 125°, 235° Quad II & Quad III

Quadrant 1 0° < < 90° = Find angle when given tan Given that 0° 360°, find when Quadrant I sign (+) (a) tan = 1. 7660 and a= 1. 7660 a = 60° 29’ Hence = 60° 29’, 180° + 60° 29’ = 60° 29’, 240° 29’ tan-1 Quadrant 2 90° < < 180° SIN (+) = 180°− Quadrant 3 180° < < 270° TAN (+) = 180°+ Quadrant 4 270° < < 360° KOS (+) = 360°− (b) tan = − 2. 5 sign (−) Quadrant 3 Quadrant 2 and Quadrant 4 a= tan-1 2. 5 a = 68° 12’ Hence = 180° − 68° 12’, 360°− 68° 12’ = 111° 48’, 291° 48’

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°