1、A； First, the value of cosa must be in the range of [- 1, 1]. First, option B can be ruled out, which is obviously not within this scope.

According to the known, point P is in the second quadrant, and the cosine value must be negative, so CD is excluded, so A is chosen.

The above method is the exclusion method. Next, let's go directly to cosa. According to the definition of cosine value, it is the value of adjacent side divided by hypotenuse. You can make a chart. If the perpendicular of the X axis intersects with the X axis at d, the triangle OPD is a right triangle with the hypotenuse Po = (OD 2+PD 2) (1/2).

= (-1) 2+2) (1/2) = 5 (1/2), so COS ∠POD = 1/5 (1/2).

Therefore, COSA =-COS ∠ POD =-1/5 (1/2). Therefore, A is selected.

2、D； Analysis: Significantly means that their values exist. For example, sine and cosine are continuous in real numbers (-∞,+∞), and their values also exist.

But for tangent and cotangent, they don't exist on the coordinate axis. From their diagrams, we can also find that the tangent can't intersect with the coordinate axis Y and the cotangent can't intersect with the coordinate axis X, so it makes sense to consider that tana can't be 90+k * 180. This problem only needs to consider 90, because it is the three internal angles of a triangle.

For options tanA and cosB, it is possible to have right angles in the triangle, so tanA may be meaningless, and tanA and cosB cannot guarantee that they must be positive numbers. TanA is negative when A is obtuse, and cosB is negative when B is obtuse.

Similarly, for option B, there is no guarantee that cosB is positive, and for option C, there is no guarantee that tanA exists and tanA is positive. For option D, tanB/2 must exist, because B can't be 180, and any angle in the triangle is between (0, 180), while B.

3、C； Analysis: A is in the second quadrant, and cosa is definitely negative. According to the value of cosa, x must be negative, so the AB option is excluded. According to the analysis of the problem 1, COSA = X/(X 2+5) (1/2) and COSA = 2 (1/2).

Solve the equation to get X =-3 (1/2). So I chose C.

4、C； Analysis: P (Sina +cosa, sinacosa) is in the second quadrant, so Sina COSA >；; 0

That is, Sina and cosa have the same symbol, that is, A can only be in the first quadrant or the third quadrant, because in these two quadrants, Sina and cosa have the same symbol. If it is in the first quadrant, then Sina+COSA >; 0, in which case p contradicts what is known in the first quadrant.

So a can only be in the third quadrant, so choose C.