If tan(theta) = -3/4 and theta lies in the second quadrant (pi/2 < theta < pi), what is the value of cos(theta)?
Answer and explanation
Correct answer: D. -4/5
- Step 1: In the second quadrant, sine is positive, cosine is negative, and tangent is negative.
- Step 2: tan(theta) = y / x = -3/4 => y = 3 and x = -4.
- Step 3: The hypotenuse r = sqrt(x^2 + y^2) = sqrt((-4)^2 + 3^2) = sqrt(16 + 9) = 5.
- Step 4: cos(theta) = x / r = -4 / 5.
Answer
-4/5.
Why not the others: '4/5' violates the negative sign of cosine in quadrant II; '-3/5' is -sin(theta) instead of cos(theta); '3/5' is sin(theta).
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