Trigonometry

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