Sin Cos Tan Formula's

Sin and Cos Formula's

Sine (sin) and Cosine (cos) formula’s are equations that are true for all possible values of the variables (angles). Here are some of the Sin and Cos Formula’s.

Sin(X) Formula, Sin(X±Y) Formula, Sin(2X) Formula, Sin(-X) Formula, Sin²(X) + Cos²(X) = 1
Sine Formula's

Cos(X) Formula, Cos(X±Y) Formula, Cos(2X) Formula, Sin²(X) + Cos²(X) = 1
Cosine Formula's

• Pythagorean Identity:

Sin²(x) + Cos²(x) = 1

This identity shows the relationship between sine and cosine squared values for any angle θ in a right triangle. It stems from the Pythagorean theorem applied to the unit circle.

• Reciprocal Identities:

Sin(x) = 1 / Cosec(x) , Cos(x) = 1 / Sec(x)

These identities represent the reciprocal relationships between sine and its reciprocal, cosecant, as well as cosine and its reciprocal, secant.

• Quotient Identities:

Tan(x) = Sin(x) / Cos(x) , Cot(x) = Cos(x) / Sin(x)

These identities express the relationships between tangent and cotangent functions with sine and cosine.

• Even and Odd Identities:

Sin(-x) = - Sin(x) , Cos(-x) = Cos(x)

Even-odd nature of sine and cosine functions. The negative of an angle in sine results in a negative sine value, while for cosine, it remains the same.

• Double Angle Identities:

Sin(2x) = 2Sin(x)Cos(x) , Cos(2x) = Cos²(x) - Sin²(x)

These formulas provide relationships between the sine and cosine of double angles in terms of the sine and cosine of the original angle.

• Sum and Difference Identities:

Sin(x+y) = Sin(x)Cos(y) + Cos(x)Sin(y),

Sin(x-y) = Sin(x)Cos(y) - Cos(x)Sin(y),

Cos(x+y) = Cos(x)Cos(y) – Sin(x)Sin(y),

Cos(x-y) = Cos(x)Cos(y) + Sin(x)Sin(y)

These identities express the sine and cosine of the sum or difference of two angles in terms of sines and cosines of the individual angles.

Tan Formula's

Here are some formula’s related to tangent;

Tan(X) Formula, Tan(2X) Formula, Tan(X±Y) Formula's, Tan(-X) Formula
Tangent Formula's

• Basic tangent formula:

Tan(x) = Sin(x) / Cos(x)

• Addition and Subtraction Tangent Formula’s:

Tan(x+y) = tan(x) + tan(y) / 1 – tan(x)tan(y), Tan(x-y) = tan(x) – tan(y) / 1 + tan(x)tan(y)

• Double Angele Tangent Formula:

Tan(2x) = 2tan(x) / 1 - tan²(x)

• Symmetric Tangent Formula:

Tan(-x) = - tan(x)

• Pythagorean Identity:

tan²(x) + 1 = Sec²(x)

Noman Yousaf

Meet Noman Yousaf, a Math graduate from University of Education Lahore Jauharabad Campus. He excels at simplifying complex math topics, teaching with clarity and making math understandable for all.

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