Cos 90 Degrees | Top Q&A

The three most familiar trigonometric ratios in trigonometric functions are the sine function, the cosine function, and the tangent function. It is usually defined for angles less than a right angle, and trigonometric functions are expressed as the ratio of the sides of a right triangle containing the angle where values ​​can be found for the lengths of the sides. different line segments around a unit circle. Typically, degrees are represented as 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. Here, let’s discuss the value of the cosine 90 degrees of zero and how the values ​​are calculated using the quadrants of a unit circle.Value of Cos 90° = 0

Cos 90 degrees

To determine the cosine function of an acute angle, consider a right triangle with the angle of interest and the sides of the triangle. The three sides of a triangle are defined as follows:

  • The opposite side is the face opposite the angle of interest.
  • The hypotenuse is the opposite side of the right angle and it must be the longest side of the right triangle
  • The side is the remaining side of a triangle that forms one side of both the preferred angle and the right angle

The cosine function of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse and the formula given by Cos = Adjacent / Hypotenuse

Origin to find the Cos value of 90 degrees using the unit circle

Let’s consider a unit circle centered at the origin of the ‘x’ and ‘y’ axes. Let P(a, b) be any point on the circle formed with angle AOP = x radians. This means the length of arc AP is equal to x. From there, we determine the values ​​of cos x = a and sin x = b.Using the unit circle, consider a right triangle OMP. By using the Pythagorean theorem, we get; OM2 + MP2 = OP2 (or) a2 + b2 = 1 Therefore, every point on the unit circle is defined as; a2 + b2 = 1 (or) cos2 x + sin2 x = 1 Note that a complete rotation sub an angle of 2π radians at the center of the circle and from the unit circle, it is defined as: ∠AOB = π / 2, ∠AOC = π and Further Reading: Which ant’s center is this ∠AOD = 3π / 2 Since all angles of a triangle are integral multiples of π / 2 and it is often called The coordinates and coordinates of the points A, B, C and D are (1, 0), (0, 1), (-1, 0) and (0, -1) respectively. We can get the 90 degree cos value using quadrant. Therefore, the value of cos 90 degrees is:Cos 90° = 0 Observe that the values ​​of the sine and cosine functions do not change if the values ​​of x and y are multiples of 2π. When we consider a complete revolution from point p, it goes back to the same point again. For triangle ABC, sides a, b, c opposite angles A, B, C are cosine law, respectively. For angle C, the law of cosine is stated as c2 = a2 + b2-2ab cos(C) Also it is easy to remember special values ​​like 0°, 30°, 45°, 60° and 90° since all values ​​are in the first quadrant. All sine and cosine functions in the first quadrant have the form √(n/2) or √(n/4). When we find the values ​​of the sine functions, it is easy to find the cosine functions. 0° = (0/4) Sin 30° = (1/4) Sin 45° = (2/4) Sin 60° = (3/4) Sin 90° = (4/4) Now now Simplify all the obtained sine values ​​and put them in tabular form: From the values ​​of the sine we can easily find the values ​​of the cosine function. Now, to find the cos values, fill them in the reverse order of the sine function values. Means Cos 0° = Sin 90° Cos 30° = Sin 60° Read more: DC Trivia #27: Batman has higher IQ than Albert Einstein & Stephen HawkingCos 45° = sin 45° Cos 60° = sin 30° Cos 90 ° = sin 0° So the value of cosine 90 degrees is zero because cos 90° = sin 0 °In the same way, we can find other order values ​​of trigonometric functions that depend on the quadrant value.

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Sample example

Question:Find the value of cos 135°Solution:Cos 135° = cos(90° + 45°) Now take the values ​​a = 90° and b = 45° By using the formula, Cos(a + b) = cos a cos b – sin a sin b So it becomes Cos 135° = cos 90° cos 45° – sin 90° sin 45° cos 135° = 0 x 1 / 2 – 1 x 1 / 2cos 135° = -1 / 2Learn For more information about 90 degree cos and trigonometric functions, visit BYJU’S and also watch interactive videos to clear doubts. Read more: People make time for what they want

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