State the value of t without the use of a calculator, given t $\in$ [0, 2?) terminates in QII. cot t =

Question

Quizplus · Accepted Answer

Since cot is adjacent over opposite, we know that in QII, the adjacent side must be negative and the opposite side must be positive. Looking at the given number, we see that the first digit after the decimal point is a 4, which tells us that the angle is between π/2 and π (since in QII, the cosine is negative and the first digit after the decimal point tells us whether the angle is between 0 and π/2 or between π/2 and π). The next two digits after the 4 are dc, which, when converted to base 16, give us 220. Finally, we know that the tangent is positive in QII (since the sine is positive and the cosine is negative), so the cotangent (which is inverse of the tangent) must also be positive. The only answer choice that satisfies all of these conditions is C (11ea7f29_4fed_4dc5_9ecd_1dfdc6bbe803_TB3307_11).

State the Value of T Without the Use of a Calculator