Tan 0 Degree | Top Q&A

Video tan 0 In what is trigonometry, the value of tan 0 is 0. The word ‘Trigonometry’ is of Greek origin and the subject was developed to solve geometry problems involving triangles. It is used to measure the sides of a triangle. Angle is the measure of rotation of a given ray about its initial point and the origin ray is called the initial edge and the final position of the ray after rotation of the origin ray is called the end edge. in the counterclockwise direction then the angle is positive and if the rotation of the ray is clockwise then the angle is negative. An angle is said to be positive if the rotation is counterclockwise and if the rotation is clockwise the angle is negative. Two types of conventions used to measure angles are Read: What is tan 0?

  • Degree measurement
  • Measure radians

In degrees measurement, consider a unit circle where the angle is given as a measure of degrees and it is denoted by the symbol ‘1°’. Each degree (1°) is divided into 60 minutes (also denoted 60′) and each minute (1′) is subdivided into 60 seconds and it is denoted 60″. Another unit for measuring angles is the radian. An angle is said to have a measure of 1 radian where the angle sub-centre is equal to the 1-unit arc length in a unit circle. In general, the trigonometric ratio expressed for an acute angle is the ratio of the sides of a right triangle.

Melt 0 degrees Value

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In a right triangle, the side opposite the right angle is called the hypotenuse, the side opposite the preferred angle is called the opposite side and the other side is called the adjacency where it forms one side of both right triangles. . angle and angle of interest. The tangent to an angle is equal to the length of the opposite side divided by the length of the adjacent side.Tan = Opposite / Adjacent Edge By expressing the tangent function in terms of sin and cos, it is given by Tan = Sin / Cos

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Generating the value of Tons

To find the value of tan 0 degrees, use the sine and cosine functions. Since tan function is the ratio of sine and cosine function, we can easily find out the values ​​of tangent with the help of sine and cosine function. Just knowing the value of the sine function, we will find the value of the cos and tan functions. There is an easy way to remember Some other tangent values ​​like tan 30, tan 60 degrees.Sin 0° = [latex]sqrt {frac {0} {4}}[/latex]Sin 30° = [latex]sqrt {frac {1} {4}}[/latex]Sin 45° = [latex]sqrt {frac {2} {4}}[/latex]Sin 60° = [latex]sqrt {frac {3} {4}}[/latex]Sin 90° = [latex]sqrt {frac {4} {4}}[/latex]Now Simplify all obtained sine values ​​and put in table form: Angle (in degrees) Read more: what is the unit of resistance si | Top Q & A0° 30° 45° 60° Read more: What time does sugarcane close 90° Sin 0 1/2 [latex]fraction {1} {sqrt {2}}[/latex] [latex]frac {sqrt {3}} {2}[/latex] 1Now find the cosine function values. It is done like this: Cos 0° = Sin 90° Cos 30° = Sin 60° Cos 45° = sin 45° Cos 60° = sin 30° Cos 90° = sin 0° Angle (in degrees) Read more : what si is the unit of resistance | Top Q & A0° 30° 45° 60° Read more: What time does sugarcane close 90° Sin 0 1/2 [latex]fraction {1} {sqrt {2}}[/latex] [latex]frac {sqrt {3}} {2}[/latex] 1 Cos 1 [latex]frac {sqrt {3}} {2}[/latex] [latex]fraction {1} {sqrt {2}}[/latex] 1/2 0 Since the tangent function is a function of a sine and a cosine function, find the values ​​of tan, which can be obtained by dividing the sine function by the cosine functions with the corresponding degree values ​​Therefore, the value solubility 0 is assumed to be 0° = Sin 0° / Cos 0° = 0/1 = 0 Similarly, Tan 30° = Sin 30° / Cos 30° = [latex]frac {frac {1} {2}} {frac {sqrt {3}} {2}} = frac {1} {sqrt {3}}[/latex]Tan 45° = Sin 45° / Cos 45° = [latex]frac {frac {1} {sqrt {2}}} {frac {1} {sqrt {2}}} = 1[/latex]Tan 60° = Sin 60° / Cos 60° = [latex]frac {frac {sqrt {3}} {2}} {frac {1} {2}} = sqrt {3}[/latex]Tan 90° = Sin 90° / Cos 90° = 1/0 = Undefined So the tabular column represents the tan function as Angles (in degrees) Read more: what is the unit of resistance | Top Q & A0° 30° 45° 60° Read more: What time does sugarcane close 90° Sin 0 1/2 [latex]fraction {1} {sqrt {2}}[/latex] [latex]frac {sqrt {3}} {2}[/latex] 1 Cos 1 [latex]frac {sqrt {3}} {2}[/latex] [latex]fraction {1} {sqrt {2}}[/latex] 1/2 0 tan 0 [latex]fraction {1} {sqrt {3}}[/latex] first [latex]sqrt {3}[/latex] Undefined In the same way, we can take other values ​​of solubility such as 180°, 270° and 360°. The trigonometric table is given below, determining all the values ​​of tan along with other trigonometric ratios. Trigonometric Ratio Table Angle (In Degrees) 0334390000 180 270 360 Angle (In Radians) 0 / 6 / 4 / 3 / 2 3π / 2 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 Unknown 0 Unknown 0 cot Unknown 3 1 1 / 3 0 Unknown 0 Unknown csc Unknown 2 √2 2 / 3 1 Unknown −1 Unknown seconds 1 2 / 3 √2 2 Unknown −1 Unknown 1

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Sample problem:

Questions 1 :

Find the value of tan 150

Solution :

To find: tan value 15° degrees Tan 15° = tan (45° – 30°) We know that the formula, tan(AB) = (tan A – tan B) / (1+ tan A tan B) Now now substitute the tan value 30° and tan 45° [latex]tan 15 ^ {circle} = tan (45 ^ {circle} -30 ^ {circle}) = (tan 45 ^ {circle} -tan 30 ^ {circle}) / (1 + tan 45 ^ {circle} tan 30 ^ {circle})[/latex] [latex]tan 15 ^ {circle} = (1-frac {1} {sqrt {3}}) / (1 + frac {1} {sqrt {3}})[/latex]So, [latex]tan 15 ^ {circle} = (sqrt {3} -1) / (sqrt {3} +1)[/latex]

Question 2:

Prove that [latex]frac {sin(x + y)} {sin(xy)} = frac {tanx + tany} {tanx-tany}[/latex]

Solution:

Okay : [latex]frac {sin(x + y)} {sin(xy)} = frac {tanx + tany} {tanx-tany}[/latex]LHS = [latex]frac {sin(x + y)} {sin(xy)} = frac {sin xcos y + cos xsin y} {sin xcos y-cos xsin y}[/latex]Now, dividing the numerator and denominator by cos x cos y, we get = [latex]frac {tan x + tan y} {tan x-tan y}[/latex]= RH So LHS = RHS [latex]frac {sin(x + y)} {sin(xy)} = frac {tanx + tany} {tanx-tany}[/latex]Visit BYJU’S for more information on tangent angles in trigonometry and related articles, and watch interactive videos to clear up doubts. Related Links Tan 90 degrees Trigonometric formula Tan 60 degrees Tan 30 degrees Read more: 24 is 75 percent of any number

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