Question

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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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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