Solved Example > No. SE 5

To prove the given identity (involving acute angles).

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Explanation:

Trigonometry (from Greek trigōnon "triangle" + metron "measure"^[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. It has applications in both pure mathematics and applied mathematics, where it is essential in many branches of science and technology.

http://en.wikipedia.org/wiki/Trigonometry

List of trigonometric identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles.

These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

Trigonometric functions

The primary trigonometric functions are the sine and cosine of an angle. These are sometimes abbreviated sin (θ) and cos (θ), respectively, where θ is the angle, but the parentheses around the angle are often omitted, e.g., sin θ and cos θ.

The tangent (tan) of an angle is the ratio of the sine to the cosine:

$\tan\theta = \frac{\sin\theta}{\cos\theta}.$

Finally, the reciprocal functions secant (sec), cosecant (csc), and cotangent (cot) are the reciprocals of the cosine, sine, and tangent:

$\sec\theta = \frac{1}{\cos\theta},\quad\csc\theta = \frac{1}{\sin\theta},\quad\cot\theta=\frac{1}{\tan\theta}=\frac{\cos\theta}{\sin\theta}.$

(Our solved example in mathguru.com uses this concept).

These definitions are sometimes referred to as ratio identities.

Pythagorean identity

The basic relationship between the sine and the cosine is the Pythagorean trigonometric identity:

$\cos^2\theta + \sin^2\theta = 1\!$ (Our solved example in mathguru.com uses this concept).

where $sin 2$ $θ$ means $(sin (θ)) 2$ .

This can be viewed as a version of the Pythagorean Theorem, and follows from the equation $x$ $2$ $+$ $y$ $2$ $= 1$ for the unit circle. This equation can be solved for either the sine or the cosine:

$\sin\theta = \pm \sqrt{1-\cos^2\theta} \quad \text{and} \quad \cos\theta = \pm \sqrt{1 - \sin^2\theta}. \,$

http://en.wikipedia.org/wiki/Trigonometry

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.