Processing math: 100%

Trigonometric Ratios of Angle A2

We will learn about the trigonometric ratios of angle A2 in terms of angle A.


How to express sin A, cos A and tan A in terms of A2?

(i) For all values of the angle A we know that, sin 2A = 2 sin A cos A

Now replacing A by A2 in the above relation then we obtain the relation as,

sin A = 2 sin A2 cos A2


(ii) For all values of the angle A we know that, cos 2A = cos2 A – sin2 A

Now replacing A by A2 in the above relation then we obtain the relation as,

cos A = cos2 A2 – sin2 A2

(iii) For all values of the angle A we know that, cos 2A = 2 cos2 A - 1 or 1 + cos 2A = 2 cos2 A      

Now replacing A by A2 in the above relation then we obtain the relation as,

cos  A = 2 cos2 A2 - 1 or 1 + cos A = 2 cos2 A2


(iv) For all values of the angle A we know that, cos 2A = 1 - 2 sin2 A or 1 - cos 2A = 2 sin2 A                                         

Now replacing A by A2 in the above relation then we obtain the relation as,

cos A = 1 - 2 sin2 A2 or 1 - cos A = 2 sin2 A2

 

(v) For all values of the angle A we know that, tan 2A = 2 tan A/1 – tan^2 A          

Now replacing A by A/2 in the above relation then we obtain the relation as,

tan A = 2tanA21tan2A2

 

(vi) For all values of the angle A we know that, sin 2A = 2 tan A/1 + tan^2 A          

Now replacing A by A/2 in the above relation then we obtain the relation as,

sin A = 2tanA21+tan2A2


(vii) For all values of the angle A we know that, cos 2A = 1 - tan^2 A /1 + tan^2 A

Now replacing A by A/2 in the above relation then we obtain the relation as,

cos A = 1tan2A21+tan2A2

Note: Formulas of trigonometric ratios of angle A in terms of angle A2 is also known as sub-multiple angle.

 Submultiple Angles






11 and 12 Grade Math

From Trigonometric Ratios of Angle A/2 to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 22, 25 03:02 PM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  2. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 20, 25 12:58 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  3. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More

  4. Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan

    Jul 19, 25 05:00 AM

    Area and Perimeter of Square and Rectangle
    We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square len…

    Read More

  5. Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes

    Jul 18, 25 10:38 AM

    Area of a Square of Side 1 cm
    Area of a closed plane figure is the amount of surface enclosed within its boundary. Look at the given figures. The shaded region of each figure denotes its area. The standard unit, generally used for…

    Read More