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trigonometry help!!!!!!!!!!!!!!!!

0 votes

x is an angle in quadrant 3 and sin (x) = 1 / 3. Find sin (3x) and cos (3x).

asked Jun 24, 2013 in TRIGONOMETRY by dkinz Apprentice

1 Answer

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The given trigonometric fuction value is sin(x) = 1/3

sin(3x) = 3sinx - 4sin3x

= 3 ( 1/3) - 4 ( 1/3)3

=  - 4 ( 1/27)  =  - 4/27.

sin (x) = 1/3 ⇒ sin2x = 1/9

sin2x + cos2x  = 1

⇒ cos2x  = 1 - sin2x

Therefore cosx = √8/9

cos(3x) = 4 cos3x - 3 cosx

= 4 (√8/3) 3- 3 ( √8/3 )

= 4 ( 8√8/27) - √8

= ( 32/27 -1) √8

= 5/27√8 = 10 √2/27.

answered Jun 24, 2013 by goushi Pupil

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