Variations in trig scales

Types of trigonometric scales

Trigonometric scales on slide rules are presented in different ways. The following table shows the main variants.

Type	Variant	Notes
Scales on stock
Scales on slide	Front face Reverse face - marks on back of stock Reverse face - slide has to be reversed	Same as with scale on front face of slide.
Differential trig scales		Patented - only on Thornton rules.

The next table looks at the suitability of these main configurations for three different types of calculations:

Multiplying the sin of an angle by a number. This occurs in a right angled triangle if you know the length of the hypotenuse and the angle and want to calculate the length of the opposite side. Example: 5 * sin (36.9°) = 3
Dividing a number by the sine of an angle. This occurs in a right angled triangle if you know the length of the side opposite the angle and wish to know the length of the hypotenuse. Example 3 / sin (36.9°) = 5
Multiplying a number by the sine of one angle and dividing it by the sine of another. This occurs if you know one length a and two angles A and B in the formula a / Sin A = b / Sin B and you wish to calculate the length b. Example 3 * sin(30°) / sin (45°) = 2.12

The following assume use of the trig scales with the C and D scales. On some rules it may be necessary to modify the instructions slightly for use with A and B scales.

Arrangement	Multiplying by function	Dividing by function	Combined multiplication and division
Trig scales on stock	Cursor to 36.9° on S scale. 10 on B scale to Cursor. Read answer, 3, on D scale against 5 on C scale.	Cursor to angle 36.9° on S scale. 3 on C scale to cursor. Read answer, 5, on C scale against 10 on D scale.	Cursor to 45° on S scale. 3 on C scale to cursor. Cursor to 30° on S scale. Read answer, 2.12, on C scale.
Trig scales on slide front face	10 on C scale to 5 on D scale. Cursor to 36.9° on S scale. Read answer, 3, on D scale against cursor.	Cursor to 3 on D scale. 36.9° on S scale to cursor. Read answer, 5, against 10 on D scale.	Cursor to 3 on D scale 45° on S scale to cursor Cursor to 30° on S scale Read answer, 2.12, on D scale.
Trig scales on reverse with marker on stock.	36.9° on S scale to mark on back Read answer, 3 on C scale, against 5 on D scale.	36.9° on S scale to mark on back Read answer, 5 on D scale, against 3 on C scale.	45.0° on S scale to mark on back Cursor to 3 on C scale. 30° on S scale to mark on back. Read answer, 2.12, on C scale.
Differential trig scales.	Cursor to 36.9° on D scale. 36.9° on Sd scale to cursor. Read answer, 3, on D scale against 5 on C scale.	Cursor to 36.9° on D scale. 36.9° on Sd scale to cursor. Read answer, 5, on C scale against 3 on D scale.	Set 45° on C scale against 30° on D scale. Cursor to 45° on Sd scale. 30° on Sd scale to cursor. Read answer, 2.12, on D scale against 3 on D scale.