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**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. |