When we learn about trigonometric formulas, we consider them for rightangled triangles only. In a rightangled triangle, we have 3 sides namely – Hypotenuse, Opposite side (Perpendicular), and Adjacent side (Base). The longest side is known as the hypotenuse, the side opposite to the angle is perpendicular and the side where both hypotenuse and opposite side rests is the adjacent side.
There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.
By using a rightangled triangle as a reference, the trigonometric functions and identities are derived:
The Reciprocal Identities are given as:
All these are taken from a rightangled triangle. When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the trigonometric functions.
Below is the table for trigonometry formulas for angles that are commonly used for solving problems.
These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called cofunction identities.
All trigonometric identities are cyclic in nature. They repeat themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is true for cos 45° and cos 225°. Refer to the above trigonometry table to verify the values.
The cofunction or periodic identities can also be represented in degrees as:
Also,
Sin 3x is the sine of three times of an angle in a rightangled triangle, which is expressed as:
Sin 3x = 3sin x – 4sin3x
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1. What are the basic trigonometric ratios? 
2. How do I find the values of trigonometric ratios for special angles? 
3. How can I find the values of trigonometric ratios for any angle? 
4. What is the Pythagorean identity in trigonometry? 
5. How are trigonometric ratios used in reallife applications? 
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