4.1.
Clockwise direction. This choice is just an agreement, not a law of nature.

4.2.
Angle 1 = 360° + 35° = 395°; Angle 2 = –35°; Angle 3 = 360° – 35° = 325°.

4.3.
500° = 360° + 140°
The angle of 140° lies in the 2^nd quadrant. Therefore, the angle of  500° also lies in
the 2^nd quadrant.

4.4.
= – 430 ° = –360° – 70°. The picture is this.

4.5.
PQ is the y-coordinate of the point P. Therefore, PQ = sin .

4.6.
1) In the 3rd quadrant sine is negative.
2) In the 4th quadrant cosine is positive.

4.7.
1) sin 180° = 0;    2) cos 180° = –1 ;    3) tan 180° = 0;    4) sin(–90°) = –1;
5) cos(–90°) = 0 ;    6) tan(–90°) is undefined;    7) cot 0° is undefined;
8) cot 180° is undefined;    9) cot(–90°) = 0;    10) cot(–270) = 0.

4.8.
tan(x + 30°) is undefined, if x + 30° = 90° + 180°· n, where n is any integer
number. Therefore, x = 60° + 180°· n.

4.9.
b) and d).

4.10.

4.11.

4.12.

4.13.
1) sin (– 50°) < 0;     2) cos(– 50°) > 0;     3) sin 200° = sin (180°+ 20°) < 0;
4) cos 200° = cos (180°+ 20°) < 0;     5) tan (– 50°) < 0;     6) cot(– 50°) < 0;
7) tan 200° = tan (180°+ 20°) > 0;     8) cot 200° = cot (180°+ 20°) > 0;

4.14.
1) Recall that sin is the y-coordinate, cos is the x-coordinate. Because
sin < 0 and cos > 0, the angle lies in the 4^th quadrant.

2) y-coordinate = sin> 0.   tan = y/x < 0 . Since y > 0, x < 0. The angle lies in the 2^nd quadrant.

4.15.
Since sin = cos, y and x-coordinates of the correspondent point are equal.

4.16.

4.17.
The first word "All" means that in the 1^st quadrant all trig functions are positive, and so on.