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Study Notes IX-XII - Notes & Assignments XI

Assingment trignomatric functions

Simple rule to remember:

ALL SCHOOL TO COLLEGE
                    OR
AFTER SCHOOL TO COLLEGE
                    OR
ADD SUGAR TO COFFEE

        

TRIGONOMETRIC RATIOS OF ANGLES (- )

1. sin(- ) = -sin
2. cos(- ) = cos
3. tan(- ) = - tan
4. cosec(- ) = - cosec
5. sec(- ) = sec
6. cot(- ) = - cot

TRIGNONOMETRIC RATIOS OF

1. sin = cos
2. cosec = sec
3. cos = sin
4. tan = cot
5. sec = cosec
6. cot = tan

TRIGONOMETRIC RATIOS OR

1. sin = cos
2. cos = -sin
3. tan = - cot
4. cosec = sec
5. sec = - cosec
6. cot = - tan

TRIGONOMETRIC RATIOS OF

1. sin = sin
2. cos = - cos
3. tan = - tan
4. cosec = cosec
5. sec = - sec
6. cot = - cot

TRIGONOMETRIC RATIOS OF

1. sin = -sin
2. cos = - cos
3. tan = tan
4. cosec = - cosec
5. sec = - sec
6. cot = tan

TRIGONOMETRIC RATIOS OF

1. sin = - sin
2. cos = cos
3. tan = - tan
4. cosec = - cosec
5. sec = sec
6. cot = - cot

TRIGONOMETRIC RATIOS OF

1. sin = sin
2. cos = cos
3. tan = tan
4. cosec = cosec
5. sec = sec
6. cot = cot

(i) For angle 0- , - , + , 2 - , 2 + , the trigonometric ratio remains to be the same.
sin (- ) = - sin , tan ( + ) = tan , cos (2 - ) = cos

(ii) For angles , , , the trigonometric ratio changes from cos to sin , tan to cot , cosec to sec and vice versa.

Example:

sin = cos
tan = cot
sec = - cosec etc.

TRIGONOMETRIC RATIOS OF (x+y)

1. sin(x + y) = sin x cos y + cos x sin y

2. cos (x + y) = cos x coy - sin x sin y
3. tan (x +y) =
4. cot (x + y) =

TRIGONOMETRIC RATIOS OF (x- y)

1. sin (x - y) = sin x cos y - cos x sin y

2. cos (x - y) = cos x cos y + sin x sin y
3. tan (x -y) =
4. cot (x - y) =

TRIGONOMETRIC RATIOS OF (2x)

1. sin 2x = 2 sin x cos x =
2. tan 2 x =
3. cos 2x = cos² x - sin² x = 2 cos² x - 1 = 1 - 2 sin² x =

TRIGONOMETRIC RATIOS OF (3 x )

1. sin 3 x = 3 sin x - 4 sin³ x

2. cos 3 x = 4 cos³ x - 3 cos x
3. tan 3 x =

Sum and Difference of two like ratios:

1. sin x + sin y = 2 sin cos
2. sin x - sin y = 2 cos sin
3. cos x + cos y = 2 cos cos
4. cos x - cos y = - 2 sin sin

Product of Trigonometric Ratios:

1. 2 sin x cos y = sin (x + y) + sin (x - y)
2. 2 cos x sin y = sin (x + y) - sin (x - y)
3. 2 cos x cos y = cos (x + y) + cos (x - y)
4. 2 sin x sin y = cos (x - y) - cos (x - y)

General Solution of an Equation

1. If sin = 0, then = n , n є
2. If cos = 0, then = (2 n + 1) , n є
3. If tan = 0, then = n , n є
4. sin = sin = n + (- 1)ⁿ , n є
5. cos = cos = 2 n , n є
6. tan = tan = n + , n є

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