Tan 30 Degrees | Top Q&A
The value of 30 degree melt is 1 / √3. The value of tan π / 6 can be evaluated with the help of a unit circle, graphically. In trigonometry, the tangent to an angle in a right triangle is equal to the ratio of the opposite and adjacent sides of the angle. The exact value of tan 30° is 0.57735 Read: what is tan 30° Tan 30° = 1 / 3 = 0.57735 The value of the tangent to the 30 degree angle can also be evaluated using the values of sine 30 degrees and cos 30 degrees . Let’s find out more details in this article.
Tan value 30 degrees
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The tangent value of 30 degrees is one in root 3 (1 / √3). Like Sine and Cosine, Tangent is also a fundamental function of trigonometry. Most trigonometric equations are based on these ratios. Usually, to find the value of the sine, cosine and tangent ratios, we use right triangles and also take an example of a unit circle. First, let’s discuss the tan value of 30 degrees in a right triangle.Assume that triangle ABC is right-angled at C, α is the angle, h is the hypotenuse, b is the adjacent side or base, and a is the opposite or perpendicular side. As we know, Tan α = Opposite / Adjacent face∴ Tan α = a / b Similarly, we can also find values for sine and cosine ratios. [Adjacent Side/Hypotenuse]∴ Cos α = b / h
Find the value of Tan 30 using the Sin and Cos . function
We can also express the tangent function as a ratio of the sine function and the cosine function.∴ Tan α = sin α / cos α Read more: What color is made from green and blue So tan 30 degrees we can write as; Tan 30° = sine 30° / cos 30° We know, Sin 30° = 1/2 & Cos 30° = 3 / 2∴ Tan 30° = (1/2) / (√3 / 2) Tan 30 ° = 1 / 3 Therefore, the value of Tan 30 degrees is 1 / 3We can also find the values of tan 0, tan 45, tan 60 and tan 90 in the same manner.Tan 0 = sin 0 / cos 0 = 0/1 = 0Tan 45 = sin 45 / cos 45 = (1 / √ 2 ) / (1 / 2) = 1Tan 60 = sin 60 / cos 60 = (√3 / 2) / (½) = 3Tan 90 = sin 90 / cos 90 = 1/0 = Unknown
Tangent to the unit circle
Unit circle: For a unit circle, we can also calculate the value of tan 30 degrees. The unit circle has a radius of 1 unit and it is plotted on the XY plane. With the chart below, you can check the value of all trigonometric ratios, such as sin, cos, tan, sec, cot and cosec.
Also, as you can see, the values are defined here in radians in the case of the unit circle and not in degrees. In the same way, we can deduce other values of tangent (0°, 45°, 60°, 90°, 180°, 270° and 360°).
Tan’s Important Angles (30, 45, 60)
In trigonometry, when we learn about angle ratios, the three main ratios are sine, cosine, and tangent. In addition, we learn these ratios in terms of angles, such as 0°, 30°, 45°, 60°, and 90°. Read more: What does Fr mean in a text. Also, learn them in radians.Tan 30 = Tan π / 6 = 1 / √3Tan 45 = Tan π / 4 = 1Tan 60 = Tan π / 3 = √3Tan 0 = 0 and tan 90 = Unknown , very easy To remember. Check out the trigonometric table below to get the values of all the trigonometric ratios. CornerRadian 0 °0 30°/ 6 45 °/ 4 60°/ 3 90°/ 2 180° 270°3π / 2 360°2π Sin 0 1/2 1 / 2 3 / 2 1 0 -1 0 Cos 1 3 / 2 1 / 2 1/2 0 -1 0 1 Tan 0 1 / 3 1 √3 0 0 Cot ∞ 3 1 1 / 3 0 0 ∞ Sec 1 2 / 3 √2 2 -1 1 Cosec 2 2 2 / 3 1 -1
Trigonometric formula based on tangent function
Keep learning with us and Download BYJU’S learning app-for interactive videos. Read more: How to cut cocaine Links related to MATHS Tan 0 Equals Trigonometric Identification Tan 60 Equals Tan 90 Degrees
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