Manual / Guide · 1955

The SRT Scale: Supplement to the Manuals on the 4081 Log Log Duplex Decitrig, 4083 Log Log Duplex Vector and 4071 Polyphase Duplex Decitrig Slide Rules

Six-page K&E supplement issued when the SRT scale replaced the ST scale (catalogue 1955b; on the rules c. 1956). Tells owners to read SRT wherever their manual says ST; revised Section 38 'Radians. Small Angles' (replaces 4081 manual sections 37-38 and 4071 manual sections 39-40): SRT is a C scale graduated 0.573-5.73 degrees so that an angle in degrees on SRT reads in radians on C; worked examples (3.56 deg = 0.0621 rad), exercises and answers.

Author: Keuffel & Esser Co.
Year: 1955
Type: Manual / Guide
Credit: Page scans by Clark McCoy, K&E Catalogs & Manuals archive (mccoys-kecatalogs.com); assembled into a PDF from the six page images.

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The SRT Scale Supplement to the Manuals on the 4081 LOG LOG DUPLEX DECITRIG® 4083 LOG LOG DUPLEX VECTOR® 4071 POLYPHASE DUPLEX DECITRIG® Slide Rules KEUFFEL & ESSER CO. Copyright 1955, by Keuffel & Esser Co. ( SRT SCALE REPLACES ST SCALE For the latest model slide rules on which the SRT scale has replaced the ST scale, wherever ST is mentioned in the instruction manuals, read SRT. The scale designated SRT is, as its name indicates, used to find sines, radian equivalents, and tangents of angles, ranging from 0.573 degrees to 5.73 degrees approximately. SECTION 38 (REVISED) The revised section 38 below replaces sections in Manuals which do not refer to the SRT scale as follows: In Manual on No. 408] Loc Loc Duptex Decrrric (used also with No. 4083 Loc Loc DupLex Vector), it replaces sections 37 and 38 (pages 62-64). In Manual on No. 4071 PotypHase Dupiex Decirric, it replaces sections 39 and 40 (pages 59-62). 38. Radians. Small Angles. A radian is an angular unit equal to (2’ or 57.3° accurate to three figures. The SRT scale is a C scale whose marks represent numbers of degrees ranging from 0.573° to 5.73° approximately. It is so folded that the following rule holds. Rule. When the hairline ts set to an angle in degrees on the SRT scale, it is also set to the same angle in radians on the C* scale, provided the number on the C scale is prefixed by “0.0” as indicated by the legend 0.01 to 0.1 at the end of the SRT scale. For example, in accordance with the rule, push hairline to 3.56° on SRT, at hairline read 621 on C. Therefore 3.56° = 0.0621 radian. * Of course the D scale may be used instead of the C scale when the rule is closed [2] Observe that if we multiply both members of the equation 3.56° = 0.0621 radian by 10, 10?, | and _! in succession, we get “ 10°” 10" eae ae (10) (3.56°) = (10) (0.0621), or 35.6° = 0,621 radian, (100) (3.56°) = (100) (0.0621), or 356° = 6.21 radians, (3) (3.56°) = (35) (0.0621), or 0.356° = 0.00621 radian, 1 F 1 aE (35) (3.56°) = (sis) (0.0621), or 0.0356° = 0.000621 radian. In general for any integer k, positive or negative 10*(3.56°) = 10*(0.0621) radian. Now using the rule in reverse, push the hairline to 1176 on C, at hairline read 0.674° on SRT, and conclude that 0.01176 radian = 0.674°. Multiplying this through by 10?, a and 10* in succession, we get 1.176 radians = 67.4°, 0.001176 radian = 0.0674°, 10* (0.01176) radians = 10* (0.674°). For angles 6 in radians, where 6 is less than 0.1 radian (or 5.73°), the following relation holds 6 radians > sin 6 = tan §, (20) where the symbol “” means “approximately equals”. In other words, the value of an angle in radians found by means of the italicized rule is also its sine and its tangent to slide rule accuracy.* For example: push hairline to 3.84° on SRT _ at hairline read 670 on C. Therefore, in accordance with the italicized rule, sin 3.84° = tan 3.84° = 0.0670, and, in agreement with equation (20), — sin 0.384° = tan 0.384° = 0.00670, sin 0.0384° = tan 0.0384° = 0.000670, and so on. * The Sr re ee eee ce rele dye aye Be boxe enke by and —0. for tan 0.1. These errors are comparable in in slide rule computation. [3] By using the relations of §25, the italicized rule, and (20), we can find the values of other trigonometric functions of small angles. For example cot 1.352° = 1/tan 1.352° = 1/sin 1.352° = esc 1.352°. Hence push hairline to 1.352° on SRT, at hairline read on C, 0.0236 & sin 1.352°, at hairline read on CI, 40.31 & cso 1.352° & cot 1.352°. Also to find cos 88.76°, use (8) §25 to get cos 88.76° = sin(90° —88.76°) = sin 1.24°. push hairline to 1.24° on SRT at hairline read 0.0216 on C. Therefore cos 88.76° = sin 1.24° = 0.0216. Then without moving the slide at hairline read 462 on CI and conclude that sec 88.76° = 1/cos 88.76° = 46.3, tan 88.76° = 1/cot 88.76° = 1/cos 88.76° = 46.3. Before beginning the exercises, the student should use the slide rule, the italicized rule of this section and (20) to verify the following approximate equations: (a) 1.272° = 0.0222 radian (f) sin 0.286° = 0.00499 (b) 12.72° = 0.222 radian (g) tan 0.286° = 0.00499 (c) 0.0531 radian = 3.04° (h) csc 0.286° = 20.0 (d) 5.31 radians = 304° (t) cot 0.286° = 20.0 (e) sin 2.86° = 0.0499 (j) sec 87.25° = 20.8 EXERCISES 1, Express in radians: (a) 1.416° (6) 0.833° (c) 2.5° (d) 2.67°. 2. Express in degrees: (a) 0.01823 radian (6) 0.0462 radian (c) 0.0865 radian 3. Express in radians: (a) 3.59° (b) 0.0359° (c) 35.9° (d) 359°. 4. Express in degrees: 5 (a) 0.0296 radian (b) 0.206 radian (c) 0.000296 radian 5. Express in radians: (a) 912° (b) 435° (ce) 0.000314° (d) 2900°. [4] 6. Find sin 3.42°, tan 3.42°, ese 3.42°, cot 3.42°. 7. Find sin 0.056", tan 0.056°, cse 0.056°, cot 0.056°. 8. Find cos 89.75°, sec 89.75°, tan 89.75°, cot 89.75°. 9. Express in degrees the following angles expressed in radians: = 3x = ¥ 5x Hint:,Since x radians = 180°, replace x by 180°. However to change = radians to degrees opposite 6 on DF set 5 of C opposite index of D read 15 on SRT, and 5«/6 radians = 150 degrees. 10. Evaluate the following: : : tan 0.2° (a) 83 sin 0.0144 (d) 00001745" b . ° sin 0.3° (b) 500 tan 0.0097 (e) S137 : ° 8 sec 88.25° 4 . patna Phase (c) 432 sin 0.716 (f) 172 11. The angles in the following exercises are in radians. Change these angles to degrees and then find the values of the functions: (a) sin 0.345 (6) tan 0.524 (c) sinl (d) cos 1 (e) sin 0.628 §=(f) esc 2 (g) cot 4.17 (hk) cos 2.81. [5] ANSWERS 1. (a) 0.0247 (6) 0.01454 (c) 0.0436 (d) 0.0466 2. (a) 1.044° (6) 2.65° (c) 4.96” 3. (a) 0.0627 (6) 0.000627 = (c) 0.627 (d) 6.27 4. (a) 1.696° (6) 16.96° (c) 0.01696° 5. (2) 15.92 (6) 7.59 (c) 0.00000548 (d) 50.6 6. 0.0597, 0.0597, 16.75, 16.75 7. 0.000977, 0.000977, 1023, 1023 8. 0.00436, 229, 229, 0.00436 9. (a) 60°, (b) 135° (c) 2.5° (d) 1° (e) 150° 10. (a) 0.0209 (6) 0.0846 (c) 5.40 (d) 20.0 (e) 0.0400 (f) 55.5 11. (a) 0.338 = (b) 0.578 (c) 0.841 (d) 0.540 (e) 0.588 (f) 1.100 = (g) 0.603 (h)-0.946 Printed in U.S.A. [6]