Above: the cot calculator output for increasing angle values in degrees. Use this cotangent calculator to easily calculate the cotangent of an angle given in degrees or radians. Opp/Adj = Tangent (tan also = sin/cos) Hyp/Opp = Cosecant. Exact Form: + if $\frac{A}{2}$ lies in quadrant | or |V - if $\frac{A}{2}$ lies in quadrant || or |V, $\cot\frac{A}{2}=\pm\sqrt{\frac{1+\cos A}{1-\cos A}}$ The result can be shown in multiple forms. The Trignometric Table of sin, cos, tan, cosec, sec, cot is useful to learn the common angles of trigonometrical ratios from 0° to 360°. Subscribe! For example, if in the illustration above b = 6 and a = 12, then cot(α) = 6 / 12 = 0.5. To use the reference angle calculator, simply enter any angle into the angle box to find its reference angle, which is the acute angle that corresponds to the angle entered. Use this simple sec calculator to calculate the sec value for 300° in radians / degrees. The period of sin is 2$\pi$. Use this simple cos calculator to calculate the cos value for 300° in radians / degrees. This website uses cookies to improve your experience, analyze traffic and display ads. Alternatively, if the angle is unknown, but the lengths of the two sides of a right angle triangle are known, calculating the cotangent is just a matter of dividing the adjacent by the opposite side. Why an angle is made up of rays and not of lines or line segments? We are not to be held responsible for any resulting damages from proper or improper use of the service. The exact value of is . Select degrees or radians in the drop down box and calculate the exact cos 300° value easily. $\sin\frac{A}{2}=\pm\sqrt{\frac{1-\cos A}{2}}$ http://www.freemathvideos.com Want more math video lessons? This is a simple trigonometric cotangent calculator to calculate the cot value in degrees or radians. Below is the trigonometry table, which defines all the values of sine along with other trigonometric ratios. Make the expression negative because sine is negative in the fourth quadrant. How do you evaluate sec 120 degrees? Free online tangent calculator. It is useful for finding an angle x when cot(x) is known. Cos 30° = √3/2 . Select degrees or radians in the drop down box and calculate the exact sec 300° value easily. It is also expressed as the square root of three divided by two. 1. Find the Exact Value csc(300 degrees ) Apply the reference angleby finding the anglewith equivalenttrig values in the first quadrant. cot (300) =. Our online calculators, converters, randomizers, and content are provided "as is", free of charge, and without any warranty or guarantee. Math tutorial for using the sum of two angles formula of sine for 105 degrees - Duration: 6:44. + if $\frac{A}{2}$ lies in quadrant | or ||| Find the Exact Value cot(330 degrees ) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°, Sum and Difference of Trigonometric Functions, Multiplication of 2 Trigonometric Functions. at the angles of 0°, 30°, 60°, 90°: How do you find the trigonometric functions of values that are greater than #360^@#? In order to calculate the cot value on the calculator, just enter the angle and select the angle type as degrees (°) or radians (rad) from the drop down select menu. - if $\frac{A}{2}$ lies in quadrant || or |V, $\tan\frac{A}{2} = \frac{\sin A}{1+\cos A} = \frac{1-\cos A}{\sin A}=\csc A-\cot A$, $\cot\frac{A}{2} = \frac{\sin A}{1-\cos A} = \frac{1+\cos A}{\sin A}=\csc A+\cot A$, $\cos(2A) = \cos^2(A) - \sin^2(A) = 2\cos^2(A) - 1 = 1 - 2\sin^2(A)$, $\tan(2A) = \frac{2\tan(A)}{1- \tan^2(A)}$, $\cos(2A) = \frac{1 - \tan^2(A)}{1 + \tan^2(A)}$, $\sin(2A) = \frac{2\tan(A)}{1 + \tan^2(A)}$, $\tan3A=\frac{3\tan A - \tan^3A}{1-3\tan^2A}$, $\cot3A=\frac{\cot^3A-3\cot A}{3\cot^2A-1}$, $\sin4A = 4\cos^3A\cdot \sin A - 4\cos A\cdot \sin^3A$, $\cos4A = \cos^4A - 6\cos^2A\cdot \sin^2A + \sin^4A$, $\tan4A=\frac{4\tan A - 4\tan^3A}{1-6\tan^2A+\tan^4A}$, $\cot4A=\frac{\cot^4A-6\cot^2A+1}{4\cot^3A-4\cot A}$, $\sin^4(A)=\frac{\cos(4A) - 4\cos(2A) + 3}{8}$, $\cos^4(A)=\frac{4\cos(2A) + \cos(4A) + 3}{8}$, $\sin(A + B) = \sin(A)\cdot \cos(B) + \cos(A)\cdot \sin(B)$, $\sin(A - B) = \sin(A)\cdot \cos(B) - \cos(A)\cdot \sin(B)$, $\cos(A + B) = \cos(A)\cdot \cos(B) - \sin(A)\cdot \sin(B)$, $\cos(A - B) = \cos(A)\cdot \cos(B) + \sin(A)\cdot \sin(B)$, $\tan(A + B) = \frac{\sin(A + B)}{\cos(A + B)}=\frac{\sin(A)\cdot \cos(B) + \cos(A)\cdot \sin(B)}{\cos(A)\cdot \cos(B) - \sin(A)\cdot \sin(B)}$, $\tan(A + B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A)\cdot\tan(B)}$, $\cot(A \pm B) = \frac{\cot(B)\cot(A)\mp 1}{\cot(B)\pm \cot(A)}=\frac{1\mp \tan(A)\tan(B)}{\tan(A)\pm \tan(B)}$, $\sin(A + B + C) = \sin A\cdot\cos B\cdot\cos C + \cos A\cdot\sin B\cdot\cos C + \cos A\cdot\cos B\cdot\sin C - \sin A\cdot\sin B\cdot\sin C$, $\cos(A + B + C) = \cos A\cdot\cos B\cdot\cos C - \sin A\cdot\sin B\cdot\cos C - \sin A\cdot\cos B\cdot\sin C $ θ°. 300 degrees is in the fourth quadrant. See our full terms of service. The graph of the tangent function on the interval 0 - $\pi$, Animated graph(open in a new window): Therefore, the exact value of cos 30 degrees is written as 0.8660 approx. - if $\frac{A}{2}$ lies in quadrant ||| or |V, $\cos\frac{A}{2}=\pm\sqrt{\frac{1+\cos A}{2}}$ Make the expression negative because cotangent is negative in the fourth quadrant. What is the value of #sin -45^@#? Sine Angle Sum Identity Sometimes, we want to find the exact value of sin( x ), where x does not have a well-known sine value, but it … In the same way, we can derive other values of sin degrees like 0°, 30°, 45°, 60°, 90°,180°, 270° and 360°. Tan (300) cot (300) =. The range of the function is [-1,1]. In the figure above, cotα = b / a, and cotβ = a / b. Cos 30° = √3/2 is an irrational number and equals to 0.8660254037 (decimal form). Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. However, the approximate value of cos of $45$ degrees is taken as $0.7071$ in mathematics. What is the sine, cosine, tangent, cotangent, cosecant, and secant of -90 degrees? Also you can calculate using the 30-60-90 triangle since 210-180=30 degrees. Make the expression negative because cotangent is negative in the fourth quadrant. The calculator automatically applies the rules we’ll review below. The graph of the tangent function on the interval 0 - 2$\pi$. - if $\frac{A}{2}$ lies in quadrant || or |||, $\tan\frac{A}{2}=\pm\sqrt{\frac{1-\cos A}{1+\cos A}}$ A useful feature is that in trigonometry, any two coterminal angles have exactly the same trigonometric values. How do you use the reference angles to find #sin210cos330-tan 135#? The period of sin is 2$\pi$. Reference Angle Calculator. The angle 210 degrees will fall in the third quadrant. For every angle A corresponds exactly one point P(cos(A),sin(A)) on the unit circle. + if $\frac{A}{2}$ lies in quadrant | or || Alternatively, if the angle is unknown, but the lengths of the two sides of a right angle triangle are known, calculating the cotangent is just a matter of dividing the adjacent by the opposite side. What is sin 150 degrees? The cotangent function is used in the ASA triangle rule (angle-side-angle). Unit Circle: For a unit circle also we can calculate the value of tan 30 degrees. Following from the definition, the function results in an undefined value at certain angles, like 0°, 180°, 360°, and so on. Our cotangent calculator accepts input in degrees or radians, so once you have your angle measurement, just type it in and press "calculate". This means that the x-coordinate is negative and the y-coordinate is negative. To calculate tan (45) degrees of a right angled triangle, we use the following equation where angle is 45: Tan(angle) = Opposite/Adjacent Tan 45 degrees is simply the ratio of the side opposite of the angle to the side adjacent to the angle. sin : R -> R Multiplyby . sin([0, 30, 45, 60, 90]) = cos([90, 60, 45, 30, 0]) = sqrt([0, 1, 2, 3, 4]/4). Start studying Unit Circle - Degrees. The reciprocal of cotangent is the tangent: tan(x), which is the ratio of the length of the opposite side to the length of the side adjacent to the angle. The cotangent is a trigonometric function, defined as the ratio of the length of the side adjacent to the angle to the length of the opposite side, in a right-angled triangle. The range of the function is [-1,1]. Your unit circle will give you sine and cosine of 330 degrees. The cosine of 30 degrees is 0.86. The cosine of an angle is calculated by dividing the length of the side of a right triangle adjacent to the acute angle by the length of the hypotenuse. If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Cotangent Calculator", [online] Available at: https://www.gigacalculator.com/calculators/cot-calculator.php URL [Accessed Date: 25 Feb, 2021]. Cos 30 degrees is written as cos 30° and has a value in fraction form as √3/2. The exact value of is . Notice csc is the inverse of sin, sec is the inverse of cos, and cot is the inverse of tan. the equivalent angle in the first quadrant would be 360 - 300 = 60 degrees. As long as the angle stays at 45 degrees, the ratio does not change and tan 45 degrees is a fixed number. −cot(60) - cot ( 60) The exact value of cot(60) cot ( 60) is 1 √3 1 3. this is a common angle that you can find the exact trigonometric functions for. $- \sin A\cdot\cos B \cdot\sin C - \cos A \cdot \sin B\cdot \sin C$, $\tan(A + B + C) = \frac{\tan A + \tan B + \tan C - \tan A\cdot \tan B \cdot \tan C}{1 - \tan A \cdot\tan B - \tan B\cdot\tan C - \tan A\cdot\tan C}$, $\textrm{ sin } A + \textrm{ sin }B = 2 \textrm{ sin }\frac{A + B}{2} \textrm{ cos }\frac{A - B}{2}$, $\textrm{ sin } A - \textrm{ sin }B = 2 \textrm{ sin }\frac{A - B}{2} \textrm{ cos }\frac{A + B}{2}$, $\textrm{ cos } A + \textrm{ cos }B = 2 \textrm{ cos }\frac{A + B}{2} \textrm{ cos }\frac{A - B}{2}$, $\textrm{ cos } A - \textrm{ cos }B = -2 \textrm{ sin }\frac{A + B}{2} \textrm{ sin }\frac{A - B}{2}$, $\tan A + \tan B = \frac{\sin(A+B)}{\cos A \cdot\cos B}$, $\tan A - \tan B = \frac{\sin(A-B)}{\cos A\cdot\cos B}$, $\cot A + \cot B = \frac{\sin(A+B)}{\sin A\cdot\sin B}$, $\cot A - \cot B = \frac{-\sin(A-B)}{\sin A\cdot\sin B}$, $\textrm{ sin }A \textrm{ sin }B = \frac{1}{2} (\textrm{ cos }(A - B) - \textrm{ cos }(A + B))$, $\textrm{ cos }A \textrm{ cos }B = \frac{1}{2} (\textrm{ cos }(A - B) + \textrm{ cos }(A + B))$, $\textrm{ sin }A \textrm{ cos }B = \frac{1}{2} (\textrm{ sin }(A + B) + \textrm{ sin }(A - B))$, $\tan A \cdot \tan B = \frac{\tan A+\tan B}{\cot A+\cot B}=-\frac{\tan A-\tan B}{\cot A-\cot B}$, $\cot A \cdot \cot B = \frac{\cot A+\cot B}{\tan A+\tan B}$, $\tan A \cdot \cot B = \frac{\tan A+\cot B}{\cot A+\tan B}$, $\sin A\sin B\sin C = \frac{1}{4}\big(\sin(A+B-C)+\sin(B+C-A)+\sin(C+A-B)-\sin(A+B+C)\big)$, $\cos A\cos B\cos C = \frac{1}{4}\big(\cos(A+B-C)+\cos(B+C-A)+\cos(C+A-B)+\cos(A+B+C)\big)$, $\sin A\sin B\cos C = \frac{1}{4}\big(-\cos(A+B-C)+\cos(B+C-A)+\cos(C+A-B)-\cos(A+B+C)\big)$, $\sin A\cos B\cos C = \frac{1}{4}\big(\sin(A+B-C)-\sin(B+C-A)+\sin(C+A-B)+\sin(A+B+C)\big)$, $\sin A = \frac{2\tan\frac{A}{2}}{1+\tan^2\frac{A}{2}}$, $\cos A = \frac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}$, $\tan A = \frac{2\tan\frac{A}{2}}{1-\tan^2\frac{A}{2}}$, $\cot A = \frac{1-\tan^2\frac{A}{2}}{2\tan\frac{A}{2}}$, $1\pm\sin A=2\sin^2\big(\frac{\pi}{4}\pm \frac{A}{2}\big)=2\cos^2\big(\frac{\pi}{4}\mp \frac{A}{2}\big)$, $\frac{1-\sin A}{1+\sin A} = \tan^2(\frac{\pi}{4}-\frac{A}{2})$, $\frac{1-\cos A}{1+\cos A} = \tan^2\frac{A}{2}$, $\frac{1-\tan A}{1+\tan A} = \tan(\frac{\pi}{4}-A)$, $\frac{1+\tan A}{1-\tan A} = \tan(\frac{\pi}{4}+A)$, $\frac{\cot A + 1}{\cot A - 1} = \cot(\frac{\pi}{4}-A)$, The graph of the tangent function on the interval 0 - 2, The values of sin, cos, tan, cot at the angles of 0°, 30°, 60°, 90°, 120°, Use your Unit Circle to help you with this one. Make the expressionnegative because cosecantis negative in the fourth quadrant. The exact value of is . It is an irrational number and equal to $0.7071067812\ldots$ in decimal form. The result can be shown in multiple forms. With the below graph, you can check the values of all the trigonometry ratios, such as sin, cos, tan, sec, cot and cosec. Cotangent Calculator. The easiest way to remember the basic values of sin and cos Adj/Hyp = Cosine. 1. It is called "cotangent" in reference to its reciprocal - the tangent function - which can be represented as a line segment tangent to a circle. Our cotangent calculator accepts input in degrees or radians, so once you have your angle measurement, just type it in and press "calculate". Hyp/Adj = Secant. cos : R -> R Find the Exact Value cot (300) cot (300) cot ( 300) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Therefore, sin 30 value is 1/2. Other than that, it has not had many practical applications since calculators became common, so you should rarely come across it. The values of sin, cos, tan, cot at the angles of 0°, 30°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360° The easiest way to remember the basic values of sin and cos at the angles of 0°, 30°, 60°, 90°: sin ([0, 30, 45, 60, 90]) = … Learn vocabulary, terms, and more with flashcards, games, and other study tools. … The unit circle has a radius as 1 unit and it is drawn on an XY plane. Find the exact value of tan 210 degree Step 1. All trigonometric functions are periodic. β = α ± 2π * k, where k is a positive integer. + if $\frac{A}{2}$ lies in quadrant | or ||| https://www.gigacalculator.com/calculators/cot-calculator.php. a) for angles measured in degrees. If you know the angle, then it is a simple calculation of the ratio between the two sides that is required to produce such an angle. How do you find the value of #cot 300^@#? Find the Exact Value sin(300) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Free trigonometry calculator - calculate trignometric equations, prove identities and evaluate functions step-by-step The Trignometric Table of sin, cos, tan, cosec, sec, cot is useful to learn the common angles of trigonometrical ratios from 0° to 360°. α. deg rad. Therefore, Sin 30 degree equals to the fractional value of 1/ 2. Important Angle Summary. A cotangent of an angle α is also equal to the ratio between its cosine and sine, so cotα = cosα / sinα. b) for angles measured in radians. Adj/Opp = Cotangent. tan(x) calculator. The cosine is a trigonometric function. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The inverse of the cotangent is the arccotangent function: arccot(x). Sin 30° = 1 / 2. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. − 1 √3 - 1 3. The value of cos of angle $45$ degrees in fraction is $\dfrac{1}{\sqrt{2}}$ exactly. Multiply 1 √3 1 3 by √3 √3 3 3. Brian McLogan 5,644 views Remember: Opp/Hyp = Sine . -√ 3. cot (300) = -√ 3 /3. β = α ± 360 * k, where k is a positive integer.
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