Trigonometric Functions in One Shot - JEE/Class 11th
Boards || Victory Batch
Physics Wallah - English
Trigonometry Formulas
Welcome to the Victory Pure English Batch for Class 11th! In this short
lecture, we will cover important trigonometry formulas and previous
year questions that are relevant to the JEE examination.
Important Formulas
• Sin 2 θ + Cos 2 θ = 1
• Sec 2 θ - Tan 2 θ = 1
• Secθ + Tanθ = 1/Secθ - Tanθ
• Cosθ + Cotθ = 1/Cosecθ - Cotθ
Remember the phrase "All Students Take Calculus" to recall which
trigonometric ratios are positive in each quadrant.
Double Angles
• Sin2θ = 2SinθCosθ or 2Tanθ / (1 - Tan 2 θ)
• Cos2θ = Cos 2 θ - Sin 2 θ or 2Cos 2 θ - 1 or 1 - 2Sin 2 θ or (1 - Tan 2 θ)
/ (1 + Tan 2 θ)
Also, remember the formula 2SinθCosθ = Sin(2θ) and the reverse
formula SinθCosθ = 1/2Sin(2θ).
Applications
When given Sin(x/2) and asked to express it in terms of Sin(x), use the
formula 2Sin(x/2)Cos(x/2).
When given Sin(x)Cos(x) and asked to express it in terms of Sin(2x) or
Cos(2x), use the formula Sin2θ = 2SinθCosθ or Cos2θ = 1 - 2Sin 2 θ.
, Tan Formulas
• Tan(a + b) = (Tan a + Tan b) / (1 - Tan a * Tan b)
• Tan(a - b) = (Tan a - Tan b) / (1 + Tan a * Tan b)
• Tan(π/4 + x) = (1 + Tan x) / (1 - Tan x)
• Cos(a + b) = Cos a * Cos b - Sin a * Sin b
• Cos(a - b) = Cos a * Cos b + Sin a * Sin b
• Sin(a + b) = Sin a * Cos b + Cos a * Sin b
• Sin(a - b) = Sin a * Cos b - Cos a * Sin b
Trigonometric Formulas
To write 1-cos(x) in terms of half angle, use the formula 2sin 2 (x/2). For
1+cos(x), use 2cos 2 (x/2).
The formulas for triple angles are sin(3a) = 3sin(a) - 4sin 3 (a) and cos(3a)
= 4cos 3 (a) - 3cos(a). Remembering the formula for tan(a+b+c) makes it
easy to derive other formulas.
The factorization formula is used to write expressions in terms of
multiplication. For example, 36 can be written as 2x2x3x3. To convert
expressions with plus or minus signs, use multiplication of sine or
cosine of something.
To remember the formulas for sine, cosine, and tangent, look for the
pattern of 2's. There is no formula for sine(c+d) or cosine(c+d). The
period of sine(x) is 2pi, while cosine(x) has a period of pi. The period of
tan(x) is 5pi and sec(x) and cosec(x) have a period of 2pi.
The domain of sine(x) and cosine(x) is all real numbers. For tan(x), the
domain cannot be odd multiples of pi/2 and for cot(x), it cannot be
even multiples of pi. The range of sine(x), cosine(x), and tan(x) is -1 to 1,
while the range of sec(x) and cosec(x) is (-∞,-1]U[1,∞).
The d factorization formula converts multiplication into addition or
subtraction. For example, 2sin(a)cos(b) can be converted into
sin(a+b)+sin(a-b).
Boards || Victory Batch
Physics Wallah - English
Trigonometry Formulas
Welcome to the Victory Pure English Batch for Class 11th! In this short
lecture, we will cover important trigonometry formulas and previous
year questions that are relevant to the JEE examination.
Important Formulas
• Sin 2 θ + Cos 2 θ = 1
• Sec 2 θ - Tan 2 θ = 1
• Secθ + Tanθ = 1/Secθ - Tanθ
• Cosθ + Cotθ = 1/Cosecθ - Cotθ
Remember the phrase "All Students Take Calculus" to recall which
trigonometric ratios are positive in each quadrant.
Double Angles
• Sin2θ = 2SinθCosθ or 2Tanθ / (1 - Tan 2 θ)
• Cos2θ = Cos 2 θ - Sin 2 θ or 2Cos 2 θ - 1 or 1 - 2Sin 2 θ or (1 - Tan 2 θ)
/ (1 + Tan 2 θ)
Also, remember the formula 2SinθCosθ = Sin(2θ) and the reverse
formula SinθCosθ = 1/2Sin(2θ).
Applications
When given Sin(x/2) and asked to express it in terms of Sin(x), use the
formula 2Sin(x/2)Cos(x/2).
When given Sin(x)Cos(x) and asked to express it in terms of Sin(2x) or
Cos(2x), use the formula Sin2θ = 2SinθCosθ or Cos2θ = 1 - 2Sin 2 θ.
, Tan Formulas
• Tan(a + b) = (Tan a + Tan b) / (1 - Tan a * Tan b)
• Tan(a - b) = (Tan a - Tan b) / (1 + Tan a * Tan b)
• Tan(π/4 + x) = (1 + Tan x) / (1 - Tan x)
• Cos(a + b) = Cos a * Cos b - Sin a * Sin b
• Cos(a - b) = Cos a * Cos b + Sin a * Sin b
• Sin(a + b) = Sin a * Cos b + Cos a * Sin b
• Sin(a - b) = Sin a * Cos b - Cos a * Sin b
Trigonometric Formulas
To write 1-cos(x) in terms of half angle, use the formula 2sin 2 (x/2). For
1+cos(x), use 2cos 2 (x/2).
The formulas for triple angles are sin(3a) = 3sin(a) - 4sin 3 (a) and cos(3a)
= 4cos 3 (a) - 3cos(a). Remembering the formula for tan(a+b+c) makes it
easy to derive other formulas.
The factorization formula is used to write expressions in terms of
multiplication. For example, 36 can be written as 2x2x3x3. To convert
expressions with plus or minus signs, use multiplication of sine or
cosine of something.
To remember the formulas for sine, cosine, and tangent, look for the
pattern of 2's. There is no formula for sine(c+d) or cosine(c+d). The
period of sine(x) is 2pi, while cosine(x) has a period of pi. The period of
tan(x) is 5pi and sec(x) and cosec(x) have a period of 2pi.
The domain of sine(x) and cosine(x) is all real numbers. For tan(x), the
domain cannot be odd multiples of pi/2 and for cot(x), it cannot be
even multiples of pi. The range of sine(x), cosine(x), and tan(x) is -1 to 1,
while the range of sec(x) and cosec(x) is (-∞,-1]U[1,∞).
The d factorization formula converts multiplication into addition or
subtraction. For example, 2sin(a)cos(b) can be converted into
sin(a+b)+sin(a-b).
