Explanation

The sum-to-product identity for cosine states that:

cos(θ) + cos(n) = 2cos((θ+n)/2)cos((θ-n)/2)

This is a fundamental identity in trigonometry, and it is used to simplify expressions involving sums of cosine functions.

Explanation

Given:

|a · b| = 6√3

|a × b| = 6

The dot product is given by:

a · b = |a| |b| cos(θ)

The cross product is given by:

|a × b| = |a| |b| sin(θ)

The ratio of the magnitudes of the cross and dot products is:

|a × b| / |a · b| = tan(θ)

6 / 6√3 = 1/√3 = tan(θ)

θ = arctan(1/√3) = 30°

Explanation

In any triangle, the greatest angle is always opposite the longest (greatest) side.

This is a basic property of triangles.

Explanation

The area of a square is given by:

Area = side × side

= 5 × 5

= 25

Explanation

π (pi) is approximately 3.14159.

The value of Pi (π) is the ratio of the circumference of a circle to its diameter.

Explanation

The Greek letter $\pi$(pronounced as Pie) represents the ratio between the circumference and the diameter of a circle.

i.e. $\frac{circumferenceofthecircle}{Itsdiameter\left(d\right)}=\pi$

$=Circumferenceofthecircle=\pi \times d$

$=2.\pi .r$

Explanation

The word "Trigonometry" comes from Greek: "trigonon" (triangle) and "metron" (measure).

It deals with the relationships between angles and sides of triangles.

The title of "father of trigonometry" is Hipparchus of Nicaea.

Explanation

1−sin2θ=cos2θ

Explanation

Rotating a square 90 degrees clockwise still results in a square because all sides and angles remain unchanged.

Explanation

A subset F of a topological space X is closed if and only if F is equal to its closure, denoted by Cl(F).