Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = -4/3 , x in quadrant II

Solution:

Given:

tan(x) = -4/3 ,

x in quadrant II

⇒ x = tan^-1(-4/3)

⇒x = 180° - tan^-1(4/3)

[ since x is in Q-2, x must be less than 180° ]

⇒ x = 180° - 71.56°

⇒ x = 108.44°

Now sin (2x) = sin (2 × 108.44°)

= sin (216.88°) = -0.6

cos(2x) = cos(2 × 108.44°)

= cos(216.88°) = -0.79

From trigonometric identitites,

we know that tan x = sin x / cos x

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

= -0.6/-0.79 = 0.75

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Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = -4/3 , x in quadrant II

Summary;

The values of sin(2x), cos(2x), and tan(2x) from the given information tan(x) = -4/3 when x in quadrant II is -0.6, -0.79 and 0.75 respectively.