Trigonometry, Applications of Trigonometry CBSE Class X Project
TRIGONOMETRY
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TRIGONOMETRY TRIGONOMETRY
description
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°. - PowerPoint PPT Presentation
Transcript of TRIGONOMETRY
TRIGONOMETRYTRIGONOMETRY
Sign for sin Sign for sin , cos , cos and tan and tan Quadrant IQuadrant I00° < ° < < 90° < 90°
Quadrant IIQuadrant II9090° < ° < < 180° < 180°
Quadrant IIIQuadrant III180180° < ° < < 270° < 270°
Quadrant IVQuadrant IV270270° < ° < < 360° < 360°
ALL (+)SIN (+)
TAN (+) COS (+)
=
Let = acute angle = 180°−
= 180°+ = 360°−
Finding angle Finding angle when given sin when given sin Given that 0° 360°, find when
sin = 0.7660
sin = −0.5736
Quadrant II90° < < 180°
SIN (+)
= 180°−
Quadrant III180° < < 270°
TAN (+)
= 180°+
Quadrant IV270° < < 360°
COS (+)
= 360°−
sign (+)
= sin-1 0.7660 = 50° (acute angle) = 50°, 130°
Quad I& Quad II
Quadrant I0° < < 90°
=
sign (−)Quad III&Quad IV
= sin-1 0.5736 = 35° = 180° + 35°, 360°−35° = 215°, 325°
Finding angle Finding angle when given cos when given cos Given that 0° 360°, find when
(a) cos = 0.7660
(b) cos = −0.5736
Quadrant 290° < < 180°
SIN (+)
= 180°−
Quadrant 3180° < < 270°
TAN (+)
= 180°+
Quadrant 4270° < < 360°
COS (+)
= 360°−
sign(+)
= cos-1 0.7660 = 40° = 40°, 360 − 40° = 40°, 320°
Quad I& Quad IV
Quadrant I0° < < 90°
=
sign (−)Quad II& Quad III= cos-1 0.5736
= 55° = 180° −55°, 180°+35° = 125°, 235°
Find angle Find angle when given tan when given tan Given that 0° 360°, find when
(a) tan = 1.7660
(b) tan = −2.5
Quadrant 290° < < 180°
SIN (+)
= 180°−
Quadrant 3180° < < 270°
TAN (+)
= 180°+
Quadrant 4270° < < 360°
KOS (+)
= 360°−
sign (+)
= tan-1 1.7660 = 60°29’Hence = 60°29’, 180° + 60°29’ = 60°29’, 240° 29’
Quadrant Iand Quadrant 3
Quadrant 10° < < 90°
=
sign (−)Quadrant 2and Quadrant 4
= tan-1 2.5 = 68°12’Hence = 180° − 68°12’, 360°−68°12’ = 111°48’, 291°48’
Practice makes perfect!!!Practice makes perfect!!!11. 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°
