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trigonometry formula
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Important Mathematical Formulas
Trigonometry
1. sin훉 = ퟏ
퐜퐨퐬퐞퐜훉 sin훉 =
퐨퐩퐩퐨퐬퐢퐭퐞퐡퐲퐩퐨퐭퐞퐧퐮퐬퐞
2. cos훉 = ퟏ
퐬퐞퐜훉 cos훉 = 퐚퐝퐣퐚퐜퐞퐧퐭
퐡퐲퐩퐨퐭퐞퐧퐮퐬퐞
3. tan훉 = ퟏ
퐜퐨퐭훉 = 퐬퐢퐧훉퐜퐨퐬훉
tan훉 = 퐨퐩퐩퐨퐬퐢퐭퐞퐚퐝퐣퐚퐜퐞퐧퐭
4. cot훉 = ퟏ
퐭퐚퐧훉 = 퐜퐨퐬훉퐬퐢퐧훉
cot훉 = 퐚퐝퐣퐚퐜퐞퐧퐭퐨퐩퐩퐨퐬퐢퐭퐞
5. sec훉 = ퟏ
퐜퐨퐬훉 sec훉 =
퐡퐲퐩퐨퐭퐞퐧퐮퐬퐞퐚퐝퐣퐚퐜퐞퐧퐭
6. cosec훉 = ퟏ
퐬퐢퐧훉 cosec훉 = 퐡퐲퐩퐨퐭퐞퐧퐮퐬퐞퐨퐩퐩퐨퐬퐢퐭퐞
7. sin2훉 + cos2훉 = 1
sin2훉 = 1 – cos2훉 (sin훉)2 = sin2훉
cos2훉 = 1 – sin2훉 (cos훉)2 = cos2훉
8. sec2훉 – tan2훉 = 1 (tan훉)2 = tan2훉
sec2훉 = 1 + tan2훉 (cot훉)2 = cot2훉
tan2훉 = sec2훉 – 1 (sec훉)2 = sec2훉
9. cosec2훉 – cot2훉 = 1 (cosec훉)2 = cosec2훉
cosec2훉 = 1 + cot2훉
cot2훉 = 1 – cosec2훉
10. sin(90˚ – 훉) = cos훉 tan(90˚ – 훉) = cot훉 sec(90˚ – 훉) = cosec훉
cos(90˚ – 훉) = sin훉 cot(90˚ – 훉) = tan훉 cosec(90˚ – 훉) = sec훉
11. sin(90˚ + 훉) = cos훉 tan(90˚ + 훉) = –cot훉 sec(90˚ + 훉) = –cosec훉
cos(90˚ + 훉) = –sin훉 cot(90˚ + 훉) = –tan훉 cosec(90˚ + 훉) = sec훉
12. sin(흅 – 훉) = sin훉 tan(흅 – 훉) = –tan훉 sec(흅 – 훉) = –sec훉
cos(흅 – 훉) = –cos훉 cot(흅 – 훉) = –cot훉 cosec(흅 – 훉) = cosec훉
13. sin(흅 + 훉) = –sin훉 tan(흅 + 훉) = tan훉 sec(흅 + 훉) = –sec훉
cos(흅 + 훉) = –cos훉 cot(흅 + 훉) = cot훉 cosec(흅 + 훉) = –cosec훉
14. sin( – 훉) = –sin훉 tan( – 훉) = –tan훉 sec( – 훉) = sec훉
cos(– 훉) = cos훉 cot( – 훉) = –cot훉 cosec( – 훉) = –cosec훉
15. sin(A + B) = sinAcosB + cosAsinB
sin(A – B) = sinAcosB – cosAsinB
cos(A + B) = cosAcosB – sinAsinB
cos(A – B) = cosAcosB + sinAsinB
tan(A + B) = 퐭퐚퐧퐀 퐭퐚퐧퐁ퟏ 퐭퐚퐧퐀퐭퐚퐧퐁
tan(A + B) = 퐭퐚퐧퐀 – 퐭퐚퐧퐁ퟏ 퐭퐚퐧퐀퐭퐚퐧퐁
16. Sin2A = 2sinAcosA = ퟐ퐭퐚퐧훉ퟏ 퐭퐚퐧ퟐ훉
cos2A = cos2A – sin2A = 1 – 2sin2A = 2cos2A – 1 = ퟏ 퐭퐚퐧ퟐ훉ퟏ 퐭퐚퐧ퟐ훉
tan2A = ퟐ퐭퐚퐧퐀
ퟏ 퐭퐚퐧ퟐ퐀 cot2A =
퐜퐨퐭ퟐ퐀 ퟏퟐ퐜퐨퐭퐀
Trigononometric Table :
훉 0˚ 30˚ 45˚ 60˚ 90˚
sin훉 0 ퟏퟐ
ퟏ√ퟐ
√ퟑퟐ
1
cos훉 1 √ퟑퟐ
ퟏ√ퟐ
ퟏퟐ
0
tan훉 0 ퟏ√ퟑ
1 √ퟑ ∞
cot훉 ∞ √ퟑ 1 ퟏ√ퟑ
0
sec훉 1 ퟐ√ퟑ
√ퟐ 2 ∞
Cosec훉 ∞ 2 √ퟐ ퟐ√ퟑ
1