Cosine Formulas

Q1: What are Cosine Formulas?

Answer:

All the formulas related to the trigonmetric ratio cosine are called cosine formulas. Some examples of cosine formulas are

• cos x = (adjacent side)/(hypotenuse)
• cos x = 1/(sec x)
• cos x = ± √(1 – sin²x)
• cos x = sin (90° – x)

Q2: What is the Pythagorean Identity of Cosine?

Answer:

In trigonometry, sin²x + cos²x = 1  is known as Pythagorean Identity for sine and cosine, rearranging this identity we can get

cos²x = 1 – sin²x

and further,

cos x = ± √(1 – sin²x)

Which is the Pythagorean Identity for Cosine.

Q3: What is a Double-Angle Formula for Cosine?

Answer:

The double angle formula for cosine is given as

cos 2x = cos²(x) – sin²(x) 

Using different formulas, we can derive other forms of double angle formula for cosine i.e.,

• cos 2x = 2 cos²(x) − 1 
• cos 2x = 1 – 2 sin²(x) 
• cos 2x = [(1 – tan²x)/(1 + tan²x)]

Q4: What is a Triple-Angle Formula for Cosine?

Answer:

The triple angle formula for trigonometric ratio cosine is given as

cos 3x = 4cos³x – 3cosx

Q5: What is Law of Cosine?

Answer:

For any triangle ABC with side a, b, and c (where a, b, and c are opposite sides to angle A, B, and C), law of cosine gives 

• cos A = (b² + c² – a²)/(2bc)
• cos B = (c² + a² – b²)/(2ac)
• cos C = (a² + b² – c²)/(2ab)

Trigonometry is a discipline of mathematics that studies the relationships between the lengths of the sides and angles of a right-angled triangle. Trigonometric functions, also known as goniometric functions, angle functions, or circular functions, are functions that establish the relationship between an angle to the ratio of two of the sides of a right-angled triangle. The six main trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometric angles are the Angles defined by the ratios of trigonometric functions. Trigonometric angles represent trigonometric functions. The value of the angle can be anywhere between 0-360°.

As given in the above figure in a right-angled triangle:

• Hypotenuse: The side opposite to the right angle is the hypotenuse, It is the longest side in a right-angled triangle and opposite to the 90° angle.
• Base: The side on which angle C lies is known as the base.
• Perpendicular: It is the side opposite to angle C in consideration.