MTH1010_09_01_1

Question

MTH1010_09_01_1

BlackTom AI · Accepted Answer

Consider the given information: cos(θ) = -3/5 and sin(θ) = 4/5. The signs tell us which quadrant θ lies in.

Option (a): 0 < θ < π/2. This is the first quadrant where both cos and sin are positive. Since cos(θ) is negative here, this interval cannot contain θ. Therefore (a) is incorrect.

Option (b): π/2 < θ < π. This is the second quadrant, where cos is negative and sin is positive. This matches the given signs exactly (cos negative, sin positive), so this interval is consistent with the information. Therefore (b) is a plausible location for θ.

Option (c): π < θ < 3π/2. This is the third quadrant, where both cos and sin are negative. The given sin(θ) is positive, so this interval cannot contain θ. Therefore (c) is incorrect.

Option (d): 3π/2 < θ < 2π. This is the fourth quadrant, where cos is positive and sin is negative. Both signs do not match the given cos(θ) = -3/5 (negative) and sin(θ) = 4/5 (positive), so (d) is incorrect.

In summary, only the interval that aligns with cos(θ) < 0 and sin(θ) > 0 is π/2 < θ < π, which corresponds to the second quadrant.

MTH1010_09_01_1

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