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# find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.

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## Answer to a math question find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.

Ali
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Certainly, if you know that cos$θ$ = 1/2 and sin$θ$ is negative, you can find the value of the tangent $tan(θ$) using the following steps: 1. First, find sin$θ$ using the information that sin$θ$ is negative. Since the cosine is positive and the sine is negative, you can use the Pythagorean identity for sine and cosine: sin$θ$ = ±√$1 - cos²(θ$) Since sin$θ$ is negative, you take the negative root: sin$θ$ = -√$1 - (1/2$²) sin$θ$ = -√$1 - 1/4$ sin$θ$ = -√$3/4$ sin$θ$ = -√3/2 2. Now that you have both cos$θ$ and sin$θ$, you can find the tangent $tan(θ$) using the definition of tangent: tan$θ$ = sin$θ$ / cos$θ$ tan$θ$ = $-√3/2$ / $1/2$ Now, divide the numerator by the denominator: tan$θ$ = -√3 So, the value of the tangent, given cos$θ$ = 1/2 and sin$θ$ is negative, is -√3.
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