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Can someone explain

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Find sin 2x, cos 2x, and tan 2x from the given information. 
csc x = 6, tan x < 0 

asked Nov 20, 2014 in TRIGONOMETRY by anonymous

1 Answer

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csc(x) = 6

Reciprocal identity of cscx is sinx.

1/sinx = 6

sinx = 1/6

tanx < 0

sinx is positive and tanx is negative in second quadrant.

From the basic trigonometric ratios, sin(θ) = (opposite side/hypotenuse)

From Pythagorean theorem,

Adjacent side = √[(hypotenuse)2 - (opposite side)2]

= √(36 - 1) = √35

cosx = (adjacent side/hypotenuse)

= -√35/6

Sin(2x) = 2 sinx cosx

= 2 (1/6)(-√35/6)

Sin(2x) = - 35/18

cos(2x) = cos2x - sin2x

= (-35/6)2 - (1/6)2= (35/36) - (1/36) = 34/36

cos(2x) = 17/18

tan(2x) = sin(2x)/cos(2x)

= (- 35/18)/(17/18)

tan(2x) = (- 35)/17.

answered Nov 20, 2014 by david Expert

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