Sec (180° + A) =

Tan (180° + A) = tan A, cot (180° + A) = cot A.

=

cosec A.

And similarly

Tan (-A) tan A, cot (-A) cot A,

Sec (-A)

=

= sec A, cosec (— A)

=

cosec A.

Although the results of Arts. 12, 15, 16, 17 have been proved from diagrams where A is less than a right angle, the

Bisect it by the straight line OB, so that ZAOB = and draw CD perpendicular to OA, meeting OB in E.

A

2'

19. To find the trigonometrical ratios of 15°, 75°, 120°,

135°, 150°.

(1.) Ratios of 120°.

√3

Sin 120° = sin (180° - 120°)

= sin 60° =

2

1

2'

√3, &c.

cos 30° =

Sin 150° sin (180°

&c.

==

1. Define a negative angle, and show that tan (-A) tan A, when A lies between 90° and 180°. 2. Trace the changes of sign of sin A. cos A through the four quadrants.

3. Trace the changes of sign of cos A + sin A, and of sin A, as A changes from 45° to 315°.

cos A

=

sin' A,

4. Assuming generally that cos 2 A cos2 A trace the changes of sign of cos 2 A as A changes from - 45° to 315°.

5. Write down the sines of 210°, 165°, 240°, - 120°.

6. Show that sin (90° + A) = cos A, and cos (90° + A) = sin A, for any value of A from 0° to 180°.