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# Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = -12/5 , x in quadrant II

**Solution:**

Given: tan(x) = -12/5

⇒ x = tan^{-1}(-12/5)

Clearly, tanx value is negative so we can say that x lies in either Q2 or Q4

But given that x lies in quadrant II

⇒ x = 180° - tan^{-1}(12/5)

⇒ x = 180° - 67.38°

⇒ x = 112.62°

Now, sin(2x) = sin(2 × 112.62) = sin(225.24) = -0.81

cos(2x) = cos(2 × 112.62) = cos(225.24) = 0.57

tan(2x) = tan(2 × 112.62) = tan(225.24)

From trignometric identities, we know that tanx = sinx/cosx

tan(2x) = sin(225.24) / cos(225.24)

tan(2x) = -0.81/0.57 = -1.42

tan(2x) = -1.42

## Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = -12/5 , x in quadrant II

**Summary:**

If tan(x) = - 12/5, x in quadrant II then sin(2x) is -0.81, cos(2x) is 0.57 and tan(2x) is -1.42

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