(1) (i) DA, BD. (ii) DB, AD. (iii) DA, CD. (iv) DC, AD.

(5) sin A=%, cos A=, tan A=2; sin B=, cos B=g, tan B=3. (7) of the smaller angle, the sine=1, cosine=13, tangent=17. Of the larger angle, the sine, cosine, tangent=. (8) Of the smaller angle, the sine, cosine= tangent=

V3
2

1

V3

Of the larger angle, the sine= cosine, tangent=√3.

√3
•
2

(2) sec increases continuously from 1 to ∞.
(3) sin A diminishes continuously from 1 to 0.
(4) cot diminishes continuously from ∞ to 0.

(14) cosec decreases continuously from ∞ to 1. (15) cot increases continuously from 0 to ∞.

(12) The first, if n be even, the third, if n be odd.

Each of these expressions changes continuously as the angle A increases from 0° to 360°, and their values are repeated at each complete revolution of the revolving line.

Their values are given below when they are zero and when they cease to increase and begin to decrease, and vice versa. The first table gives also the sign of each between the values.

The following figures exhibit the changes in the sign and magnitude of sin 0 (fig. i.), cos 0 (fig. ii.), and tan ✪ (fig. iii.). The measure of the distance from 0 along the line OX=the circular measure of the angle; the vertical distance from OX measures the Ratio.