. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . sin45° = —= cos45°: V21 to V2 V2 cot45°m sec 45° = V2. cosec 45°=V2. tan 45° =^=™ = m = 1. 27. To find the Trigonometric Func-tions of 60° and 30°.—Let AB be an equilateral triangle. Draw AD perpen-dicular to BC. Then AD bisects theangle BAC and the side BC. ThereforeBAD = 30°, and ABD = 60°.. 32 LetThen PLANE = 2m. ,\ BD = m. AD = V4m2 — m2 = m V3. .\ sin 60° = AD:=mV5AB : 2m = ±V3. cosec60°=- V3 cno BD 1 cos 60 = — = —BA 2 .-. sec 60° = 2. tan60°=^ =
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . sin45° = —= cos45°: V21 to V2 V2 cot45°m sec 45° = V2. cosec 45°=V2. tan 45° =^=™ = m = 1. 27. To find the Trigonometric Func-tions of 60° and 30°.—Let AB be an equilateral triangle. Draw AD perpen-dicular to BC. Then AD bisects theangle BAC and the side BC. ThereforeBAD = 30°, and ABD = 60°.. 32 LetThen PLANE = 2m. ,\ BD = m. AD = V4m2 — m2 = m V3. .\ sin 60° = AD:=mV5AB : 2m = ±V3. cosec60°=- V3 cno BD 1 cos 60 = — = —BA 2 .-. sec 60° = 2. tan60°=^ = 2?LV3 = V3. BD m cot 60° = vers 60°= 1 - cos 60°= 1 - - = 1. 2 2 V3 Also sin30» = ?5 = -*»- = !. AB 2m 2 .-. cosec30°=2. cos 30°: ,AD_mV3: AB tan 30° =5*5 = 2mm 1 DA mV3 V3 EXAMPLES. Sec 30° = —.V3 cot30°=V3. 1. Given sin0 = -; find the other5 trigonometric functions. Let BAC be the angle, and BC beperpendicular to AC. Represent BCby 3, AB by 5, and consequently AC £by V25-9 = 4. Then COs0 = A§4 AB 5 a AB 5SeC* = AC = 4 a AB 5cosec0 = - = -. >iB REDUCTION OF FUNCTIONS. 33 o 3 5 2. Given sin 0 = -; find tan 6 and cosec ft Ans. -> -• 5 4 o 3. Given cos0 = -; find sin 6 and cot ft fV2, —— • o 2\2 1 Vl5 4. Given sec# = 4; find cot 6 and sin 0. Vl5 5. Given tan 0 = V3; find sin 6 and cos ft \ V3, -• 12 5 6. Given sin 6 = —; find cos 0. — • 13 -L^ 7. Given cosec 6 = 5
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
