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Find all angles in the first four quadrants whose tangent equals cos(135 deg), and state their sine and cosine. (cos 135 deg = -1/sqrt(2).)

1. Two angles: one in Q2 and one in Q4, with tan = -1/sqrt(2); sin = +/-1/sqrt(3), cos = -/+sqrt(2)/sqrt(3)
2. One angle only, in Q1, with sin = cos = 1/sqrt(2)
3. Four angles, one in each quadrant, all with tan = +1/sqrt(2)
4. No such angle exists

Correct answer: Two angles: one in Q2 and one in Q4, with tan = -1/sqrt(2); sin = +/-1/sqrt(3), cos = -/+sqrt(2)/sqrt(3)

Solution

tan(theta) = -1/sqrt(2) is negative, so solutions lie in Q2 and Q4; from the right-triangle ratios sin and cos follow with appropriate signs.

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