If sine theta almost equal to negative 0 point 7 6 6 0 , which of the following represents an approximate value of tangent theta , for 180 degrees is less than theta comma theta is less than 270 degrees ?

Since 180° < θ < 270°, θ is in the third quadrant, where sine and cosine are both negative, so tangent is positive. Using sin²θ + cos²θ = 1, |cos θ| ≈ √(1 − 0.7660²) ≈ 0.6428. Therefore, tan θ = sin θ / cos θ ≈ (−0.7660)/(−0.6428) ≈ 1.1916, which is choice B.

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