In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse. If the angle of a right triangle is 30 degrees, and the value of the cosine at this angle i.e. the value of the 30 degree angle in fraction form is √3 / 2. It should be noted that the value of Sec 30 will be the reciprocal of Cos 30 value.
Cos Value 30
Cos 30 degrees is written as cos 30° and has a fractional value of √3 / 2. Read: what is cos 30 degreesCos 30° = 3 / 2Cos 30° = √3 / 2 is irrational and equals 0334390000 (decimal). Therefore, the exact value of cos 30 degrees is written as 0.8660 The interval √3/2 is the value of Cos 30°, which is the trigonometric ratio or trigonometric function of a particular angle.
Another alternative form of Cos 30° is pi/6 or /6 or Cos 33 (⅓) g
Cos 30 degree proof
Now that you know the value of Cos 30 degrees, let’s explore how to calculate this value. We will study two approaches to calculating that value.
Theoretical approach Knowing the property that the length of the opposite side is half the length of the hypotenuse – The property of a right triangle gives an angle equal to 30 degrees in a given right triangle As you know those two sides are the lengths of the opposite side and the hypotenuse but the third face is not yet know ie adjacent faces. We need to find this face to find the value of Cos 30 degrees.Read more: what is eating my pepper at night | Top Q & AWe will use the Pythagorean theorem to find the value of this third side In triangle AOB, AO 2 = AB2 + AB2Hypotenuse = d Opposite side = d / 2d2 = (d / 2) 2 + AB2d2 = d2 / 4 + AB2d2 – d2 / 4 = AB2 (4d2 – d2) / 4 = AB23d2 / 4 = AB2Sqrt (3) xd / 2 = ABAB / d = √ (3) / 2 Since d is the length of the opposite side, so Adjacent length / hypotenuse = √ 3 / 2Read more: How to delete Tavanero Search (Virus Removal Guide) | Top Q & AT The value of angle BOA in a given right triangle is pi/6 and the ratio given by definition of the cosine ratio represents the value of Cos 30 degreesCos 30° = Adjacent side length / side length hypotenuse = 3 / 2 = 0334390000Practical approachAnother way to calculate the value of degrees Cos 30 is through a practical approach. So if we make a right triangle using constructions, Cos pi/6 can be calculated.Step 1: Mark a point P on the plane and draw a line on it horizontally.Step 2: With the help of a protractor, make an angle of 300 with center P and take the baseline as the line drawn in step 1.Step 3: Use a ruler to create a 30 degree angle.Step 4: Use a compass to draw an arc on a line at a 30 degree angle of any length. Mark that point as Q.Step 5: From Q draw a line perpendicular to the bottom surface (horizontal line). Mark it as R (Intersection of the perpendicular to the base face.) Now after drawing a right triangle POQ we can calculate the value of Cos 30 degrees.Cos 30° = Side length / length hypotenuse = OP / OQ In the above structure, the length of side OP is taken as 7.5 cm and the length of the adjacent side is unknown. But if we measure it with a ruler, it will be 6.5 cm.Cos 30° = OP / OQ = 6.5 / 7.5 = 0.866666… Follow BYJU’S to learn math in a fun and engaging way most leading. What tattoo is it?
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