Cos Square Theta Formula

Cos Square theta Formula

Cos Square Theta Formula is the trigonometric symbol used in Mathematics. The functions of angles, i.e. the relationship between angles and sides, are given by trigonometric functions. There are usually six of these triangular symbols. Sine or sine, cosine or cosine, tangent or tangent, cotangent or cot, cosecant to cosec, and secant or sec in a right triangle. Therefore, these triangle symbols are commonly used to calculate sides and angles. In this article, a closer look has been taken at one of these trigonometric symbols, the Cos Square Theta Formula

The relationship between the base angles and sides of a triangle is represented by trigonometric functions. Also known as the angle of function. Sine, cosine, tangent, cotangent, cos, and cosec are the basic trigonometric functions. Different angles have different values ​​for the trigonometric function, Cos Square Theta Formula x. The angle varies from 0 to 360. The different angles to get the value of the function are 0, 30, 60, 90, 180, and 360 degrees. There are several key trigonometric ratios to classify the cos-squared-theta trigonometric functions. Cos Square X The main trigonometric ratios are sine, cosine and tangent. These trigonometric functions of the Cos Square Theta Formula and first-order ratios are also needed to solve sums of calculus. As we will learn, there are basically three trigonometric ratios or functions, sin x, cos x, tan x, cos squared theta, and sin squared theta, known as double angle formulas. They have double horns. 

The main goal here is to help students get good grades. If students pursue the application of trigonometric functions, they will surely get good grades. Trigonometric functions such as sine, cosine and tangent are very important and related. These functions are useful for solving various Mathematics problems. These trigonometric functions and their formulas are easy to remember and very interesting to apply to Mathematics.

What are Trigonometric Ratios?

A trigonometric ratio is a trigonometric function value based on the aspect ratio values ​​of a right-angled or rectangular triangle. 

  • Hypotenuse (longest side)
  • Perpendicular line (opposite side of the hypotenuse)
  • base (adjacent side of angle considered)

Trigonometric ratios are defined as:

 “The aspect ratio of a right triangle to one of its acute angles is known as the trigonometric ratio of that particular angle.”


cosine or cosine

tangent or tan

cosecant or cosec

secant or second


The Cos Square Theta Formula for this rationing is explained in advance on the Extramarks website. 

In the figure, a right triangle is given, and its proportions are taken with respect to the angle C.

The formula looks like this:

Sine = Perpendicular/Hypotenuse = AB/AC

cosine = base/hypotenuse = BC/AC

Tangent = Vertical/Base = AB/BC

cosec= 1/sin = hypotenuse/perpendicular = AC/AB

secant = 1/cos = hypotenuse/base = AC/BC

cotangent = 1/tan = base/perpendicular = BC/AB

Cos Square Theta Formula

The basic Cos Square Theta Formula is

cos2θ + sin2θ = 1

where the basic Cos Square Theta Formula फॉर –

sin = perpendicular/hypotenuse and

os = base/hypotenuse.

Right-shifting the sin-squared x in the above formula gives the cos-squared x formula. So the formula is

cos2x = 1 – sin2x

another formula derived from the Cos Square Theta Formula above is:

  • cos2θ = 1 – sin2θ
  • cos2θ = cos2θ – sin2θ
  • cos2θ = 2cos2θ – 1

Examples of Cos squared theta formula

Find the value of cosθ, given the value of sinθ, is 4/5.

Solution: Given, the value of sinθ = 3/5

Using cos square formula, we get

cos2θ + sin2θ = 1

cos2θ = 1 – sin2θ = 1 – (4/5)2 = 1 – 16/25

cos2θ = 9/25

cosθ = √(9/25) = ± 3/5

Thus, the value of cosθ is ± 3/5

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FAQs (Frequently Asked Questions)

1. What are trigonometric ratios?

Trigonometric functions of triangles are also called trigonometric ratios-Sine, cosine, and tangent are the three basic trigonometric ratios, also Sine is abbreviated as sin, cosine as cos, and tangent as tan. Sine, cosine and tangent are also widely used in the world of trigonometric functions in Mathematics and physics. Let’s understand with the help of right triangles. We all know that one side of a right triangle is 90°. The bottom surface is called the adjacent surface. The vertical side is called the counter. The left side is called the hypotenuse. 

2. Why is cosθ or cos2θ important in trigonometric functions?

All periodic and aperiodic functions have their own meaning in the world of trigonometry. Cosine is also a periodic function and has wide applications in Mathematics. We can understand the cosine function with the help of the unit circle. The easiest way to understand the cosine function. First, draw a unit circle on coordinates centred at the angle θ. The right side has the positive x-axis and the left side has the negative x-axis. The positive y-axis is (0, sineθ). The positive x-axis is (cosθ, 0). The hypotenuse is (cosθ, sinθ). 

3. How are the trigonometric functions defined?

Cosine, sine and tangent are the main trigonometric functions. cos theta squared is used in various trigonometry calculations. Trigonometric calculations can be performed using the six trigonometric ratios used in trigonometry. These trigonometric ratios can be used to solve or derive almost any trigonometric calculation. Sine, cosine, tangent, cotangent, cos, and cosec are some of the trigonometric functions, where sine and cosine are basic ratios. Tan, cot, and sec are derived functions. Several ratios exist for sine, cot and tan. Sinx = opposite/hypotenuse. Cosx = adjacent/hypotenuse. Tanx = sinx/cosx.