mypotant ieas) TRIGONOMETRY
Comyette Handlwrtflen Notes
* TRIGONOMETRIC IDENTITIES
VALUE TABLE
Sin' + coste = 1 → TRICKS
30° 45 6090°
t Sin' + cos'0 =1 → Trigonometric Ratios 2) 1 + tan' = sec *.. Square + Square = 1 Sine 0 1
J * 1+ tan' Sec'0 (3) 1 + cot0 cosec0 (sint9 + coste)
* 1+ cot0 = cosec'e
A
sin =E
H
cosec O=
Cos 1 8
8
o
sec'0 -tan' = 1 2. Add1 = Square
* tan = Sin0
coS6
hypote otenuse Cos B
H Cosece- cot 0 =1 (1+ tan9 = sect0)
tane 1
cosO dclote Cosece 2
cot
Sine
(P)
tan cot B (6) tan 9 Sin 3. Sec- tan = 1
CoSe Sec0 1 2
1
cose QUADRANTS ) cot 9 = Cos0
Sine
*. Cosec -cot=1 cot 1
Base (B)
1_ 1
Sec * Learn in Pairs for TRICK To REMEMBER
Sine
* TRICKs Sin, cosec (+) ALL + cose
* Sin (9o*-6) = cos |1. Sin → (opposite/ hypoteruse) (90° to 180) (0° to 9o)
(9) cosec O = 1
Sine
Easy Memory 30° 45
J
60°
3 * cos (90*-e) = Cos
Sign Rule 1 2 4
2. cose→ (base / hypotenuse) IV (10) Sin (90*- 0) = cos All →I
★ cos (90°-0) Sin tan, cot (+) cos, sec (+)
3. tan → (opposite / base) (270° to 360) (11) cos (90°- 0) = Sin Sin
* tan (90*-0) cot (180° to 27ở') Tan II (Vo.. Vī, V2, 3. J4)
Cos → IV
*IMPORTANT FORMULAS t * TRIGONOMETRY TRICKS *
1) sin (-0) = - sin Compound Angle Formulas Multiple Angle Formulas ) 90- Rule 2) Even -Odd Rule Right Triangle Trick
2) cos (- 0) = cos Sin 20 2 sin cose
3) tan (-0) = - tan Sin (A t B) SinA cosB± cosA sinB Sin (90°-0) cos0
Sin - Odd If tan0 =x
4 Sin ( -) = sin Cos (A t B) = coSA CosB T sinA sinB Cos 20 Cos- sin'0 Cos (90*- e) Sin9 Then
2cos0 -1 cos - Even 1
(5) cos (T - 0) n -Cos tan (90-e) = cot0
tan(A t B) = tanA ± tanB - 1- 2sin'0 tan - Odd
6) tan (T-0) = -tan cot (90-0) tan B= 1
) sin ( +0) = - Sin
17 tanA tanB
tan 20 = 2 tan
1- tan' e
Sec (90-0) = osec H Vitx
8) cos (T +) = -cos Cosec(90-0) = sec0 W1-x*
PRODUCT TO SUM & SUM TO PRODUCT
() tan (T +0) = tan
Memory Line
(10) Sin (2T-0) = - Sin sinA + sinB 2 sin (18) cos ( ★ BEST TRICKS
) Small Angle Values 5)_Quick Values
11) cos (2T-0) = cose 1. Learm Identities in Pairs Sin → Perpendicular
(12) tan (2T-0) = -tan sinA - sin8 - 2 cos (at) sin () 2. Learn Table Perfectty tan 30 - Cos → Base
Sin (in radian) Tan → Perpendicular
(13) tan0. cot = 1 cosA + cosB - 2 cos () cos () 3. Practice Questions Daily tan tan 45° = 1 Cot → Base
4. Use Quadrant Rule
tan 60° = /3 Sec → Hypotenuse
coSA - cos8 =z -2 sin (At) sin () 5. Write ormulas Daily
For Small Cosec → Hypotenuse
Comyette Handlwrtflen Notes
* TRIGONOMETRIC IDENTITIES
VALUE TABLE
Sin' + coste = 1 → TRICKS
30° 45 6090°
t Sin' + cos'0 =1 → Trigonometric Ratios 2) 1 + tan' = sec *.. Square + Square = 1 Sine 0 1
J * 1+ tan' Sec'0 (3) 1 + cot0 cosec0 (sint9 + coste)
* 1+ cot0 = cosec'e
A
sin =E
H
cosec O=
Cos 1 8
8
o
sec'0 -tan' = 1 2. Add1 = Square
* tan = Sin0
coS6
hypote otenuse Cos B
H Cosece- cot 0 =1 (1+ tan9 = sect0)
tane 1
cosO dclote Cosece 2
cot
Sine
(P)
tan cot B (6) tan 9 Sin 3. Sec- tan = 1
CoSe Sec0 1 2
1
cose QUADRANTS ) cot 9 = Cos0
Sine
*. Cosec -cot=1 cot 1
Base (B)
1_ 1
Sec * Learn in Pairs for TRICK To REMEMBER
Sine
* TRICKs Sin, cosec (+) ALL + cose
* Sin (9o*-6) = cos |1. Sin → (opposite/ hypoteruse) (90° to 180) (0° to 9o)
(9) cosec O = 1
Sine
Easy Memory 30° 45
J
60°
3 * cos (90*-e) = Cos
Sign Rule 1 2 4
2. cose→ (base / hypotenuse) IV (10) Sin (90*- 0) = cos All →I
★ cos (90°-0) Sin tan, cot (+) cos, sec (+)
3. tan → (opposite / base) (270° to 360) (11) cos (90°- 0) = Sin Sin
* tan (90*-0) cot (180° to 27ở') Tan II (Vo.. Vī, V2, 3. J4)
Cos → IV
*IMPORTANT FORMULAS t * TRIGONOMETRY TRICKS *
1) sin (-0) = - sin Compound Angle Formulas Multiple Angle Formulas ) 90- Rule 2) Even -Odd Rule Right Triangle Trick
2) cos (- 0) = cos Sin 20 2 sin cose
3) tan (-0) = - tan Sin (A t B) SinA cosB± cosA sinB Sin (90°-0) cos0
Sin - Odd If tan0 =x
4 Sin ( -) = sin Cos (A t B) = coSA CosB T sinA sinB Cos 20 Cos- sin'0 Cos (90*- e) Sin9 Then
2cos0 -1 cos - Even 1
(5) cos (T - 0) n -Cos tan (90-e) = cot0
tan(A t B) = tanA ± tanB - 1- 2sin'0 tan - Odd
6) tan (T-0) = -tan cot (90-0) tan B= 1
) sin ( +0) = - Sin
17 tanA tanB
tan 20 = 2 tan
1- tan' e
Sec (90-0) = osec H Vitx
8) cos (T +) = -cos Cosec(90-0) = sec0 W1-x*
PRODUCT TO SUM & SUM TO PRODUCT
() tan (T +0) = tan
Memory Line
(10) Sin (2T-0) = - Sin sinA + sinB 2 sin (18) cos ( ★ BEST TRICKS
) Small Angle Values 5)_Quick Values
11) cos (2T-0) = cose 1. Learm Identities in Pairs Sin → Perpendicular
(12) tan (2T-0) = -tan sinA - sin8 - 2 cos (at) sin () 2. Learn Table Perfectty tan 30 - Cos → Base
Sin (in radian) Tan → Perpendicular
(13) tan0. cot = 1 cosA + cosB - 2 cos () cos () 3. Practice Questions Daily tan tan 45° = 1 Cot → Base
4. Use Quadrant Rule
tan 60° = /3 Sec → Hypotenuse
coSA - cos8 =z -2 sin (At) sin () 5. Write ormulas Daily
For Small Cosec → Hypotenuse
