STD X – TRIGONOMETRY – NEWTON

TRIGONOMETRICAL IDENTITIES

In maths, an “identity” is an equation which is always true. These can be “trivially” true, like “x = x” or usefully true, such as the Pythagorean Theorem “a² +b² = c²” for right triangles or the identity (a + b) ² = a² + b² + 2ab.

These identities are useful whenever expressions involving trigonometric functions need to be simplified. If an equation involving trigonometric ratios of an angle A is true for all values of A, then that equation is called a trigonometric identity.

TRIGONOMETRICAL RATIOS

The ratios of the sides in a right triangle with respect to its acute angles are called trigonometric ratios of the angle. The angles 0⁰,30⁰,45⁰,60⁰ and 90⁰ are useful angles in trigonometry, and their numerical values are easy to remember.

When two angles add up to 90⁰, then any one angle is the complement of the other. Trigonometric ratios of complementary angles help in simplifying problems.

HEIGHTS AND DISTANCE

You are standing in front of a building and you want to measure its height. How will you do that? It is definitely not possible to measure it directly. Trigonometry helps do that. You can use angle of elevation and depression to measure heights and distances easily which are otherwise complicated to measure.

Angle of elevation

• The line of sight is the line drawn from the eye of an observer to the point on the object viewed by the observer (the line AB)
• Angle of elevation(∠BAC) is the angle between the horizontal and the line of sight to an object above the horizontal.

Angle of depression

Angle of depression is the angle between the horizontal and the line of sight to an object beneath the horizontal.

Using trigonometric ratios like tan θ and cot θ, we can compute the height or length of an object or the distance between two distant objects.