$- \sin A\cdot\cos B \cdot\sin C - \cos A \cdot \sin B\cdot \sin C$, $\tan(A + B + C) = \frac{\tan A + \tan B + \tan C - \tan A\cdot \tan B \cdot \tan C}{1 - \tan A \cdot\tan B - \tan B\cdot\tan C - \tan A\cdot\tan C}$, $\textrm{ sin } A + \textrm{ sin }B = 2 \textrm{ sin }\frac{A + B}{2} \textrm{ cos }\frac{A - B}{2}$, $\textrm{ sin } A - \textrm{ sin }B = 2 \textrm{ sin }\frac{A - B}{2} \textrm{ cos }\frac{A + B}{2}$, $\textrm{ cos } A + \textrm{ cos }B = 2 \textrm{ cos }\frac{A + B}{2} \textrm{ cos }\frac{A - B}{2}$, $\textrm{ cos } A - \textrm{ cos }B = -2 \textrm{ sin }\frac{A + B}{2} \textrm{ sin }\frac{A - B}{2}$, $\tan A + \tan B = \frac{\sin(A+B)}{\cos A \cdot\cos B}$, $\tan A - \tan B = \frac{\sin(A-B)}{\cos A\cdot\cos B}$, $\cot A + \cot B = \frac{\sin(A+B)}{\sin A\cdot\sin B}$, $\cot A - \cot B = \frac{-\sin(A-B)}{\sin A\cdot\sin B}$, $\textrm{ sin }A \textrm{ sin }B = \frac{1}{2} (\textrm{ cos }(A - B) - \textrm{ cos }(A + B))$, $\textrm{ cos }A \textrm{ cos }B = \frac{1}{2} (\textrm{ cos }(A - B) + \textrm{ cos }(A + B))$, $\textrm{ sin }A \textrm{ cos }B = \frac{1}{2} (\textrm{ sin }(A + B) + \textrm{ sin }(A - B))$, $\tan A \cdot \tan B = \frac{\tan A+\tan B}{\cot A+\cot B}=-\frac{\tan A-\tan B}{\cot A-\cot B}$, $\cot A \cdot \cot B = \frac{\cot A+\cot B}{\tan A+\tan B}$, $\tan A \cdot \cot B = \frac{\tan A+\cot B}{\cot A+\tan B}$, $\sin A\sin B\sin C = \frac{1}{4}\big(\sin(A+B-C)+\sin(B+C-A)+\sin(C+A-B)-\sin(A+B+C)\big)$, $\cos A\cos B\cos C = \frac{1}{4}\big(\cos(A+B-C)+\cos(B+C-A)+\cos(C+A-B)+\cos(A+B+C)\big)$, $\sin A\sin B\cos C = \frac{1}{4}\big(-\cos(A+B-C)+\cos(B+C-A)+\cos(C+A-B)-\cos(A+B+C)\big)$, $\sin A\cos B\cos C = \frac{1}{4}\big(\sin(A+B-C)-\sin(B+C-A)+\sin(C+A-B)+\sin(A+B+C)\big)$, $\sin A = \frac{2\tan\frac{A}{2}}{1+\tan^2\frac{A}{2}}$, $\cos A = \frac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}$, $\tan A = \frac{2\tan\frac{A}{2}}{1-\tan^2\frac{A}{2}}$, $\cot A = \frac{1-\tan^2\frac{A}{2}}{2\tan\frac{A}{2}}$, $1\pm\sin A=2\sin^2\big(\frac{\pi}{4}\pm \frac{A}{2}\big)=2\cos^2\big(\frac{\pi}{4}\mp \frac{A}{2}\big)$, $\frac{1-\sin A}{1+\sin A} = \tan^2(\frac{\pi}{4}-\frac{A}{2})$, $\frac{1-\cos A}{1+\cos A} = \tan^2\frac{A}{2}$, $\frac{1-\tan A}{1+\tan A} = \tan(\frac{\pi}{4}-A)$, $\frac{1+\tan A}{1-\tan A} = \tan(\frac{\pi}{4}+A)$, $\frac{\cot A + 1}{\cot A - 1} = \cot(\frac{\pi}{4}-A)$, 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°, The exact value of is . Use this cotangent calculator to easily calculate the cotangent of an angle given in degrees or radians. $\sin\frac{A}{2}=\pm\sqrt{\frac{1-\cos A}{2}}$ sin([0, 30, 45, 60, 90]) = cos([90, 60, 45, 30, 0]) = sqrt([0, 1, 2, 3, 4]/4). How do you find the trigonometric functions of values that are greater than #360^@#? Learn vocabulary, terms, and more with flashcards, games, and other study tools. + if $\frac{A}{2}$ lies in quadrant | or |V For every angle A corresponds exactly one point P(cos(A),sin(A)) on the unit circle. 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. 1. Therefore, the exact value of cos 30 degrees is written as 0.8660 approx. The inverse of the cotangent is the arccotangent function: arccot(x). Select degrees or radians in the drop down box and calculate the exact cos 300° value easily. Tan (300) cot (300) =. Free online tangent calculator. However, the approximate value of cos of $45$ degrees is taken as $0.7071$ in mathematics. 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. β = α ± 2π * k, where k is a positive integer. Make the expression negative because sine is negative in the fourth quadrant. −cot(60) - cot ( 60) The exact value of cot(60) cot ( 60) is 1 √3 1 3. Use this simple cos calculator to calculate the cos value for 300° in radians / degrees. Following from the definition, the function results in an undefined value at certain angles, like 0°, 180°, 360°, and so on. How do you evaluate sec 120 degrees? Other than that, it has not had many practical applications since calculators became common, so you should rarely come across it. tan(x) calculator. Important Angle Summary. 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. The angle 210 degrees will fall in the third quadrant. Your unit circle will give you sine and cosine of 330 degrees. - if $\frac{A}{2}$ lies in quadrant || or |V, $\cot\frac{A}{2}=\pm\sqrt{\frac{1+\cos A}{1-\cos A}}$ What is the value of #sin -45^@#? Cotangent Calculator. https://www.gigacalculator.com/calculators/cot-calculator.php. The graph of the tangent function on the interval 0 - $\pi$, Animated graph(open in a new window): 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. As long as the angle stays at 45 degrees, the ratio does not change and tan 45 degrees is a fixed number. The Trignometric Table of sin, cos, tan, cosec, sec, cot is useful to learn the common angles of trigonometrical ratios from 0° to 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. The value of cos of angle $45$ degrees in fraction is $\dfrac{1}{\sqrt{2}}$ exactly. the equivalent angle in the first quadrant would be 360 - 300 = 60 degrees. Find the Exact Value sin(300) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. - if $\frac{A}{2}$ lies in quadrant ||| or |V, $\cos\frac{A}{2}=\pm\sqrt{\frac{1+\cos A}{2}}$ Use this simple sec calculator to calculate the sec value for 300° in radians / degrees. This is a simple trigonometric cotangent calculator to calculate the cot value in degrees or radians. Opp/Adj = Tangent (tan also = sin/cos) Hyp/Opp = Cosecant. sin : R -> R It is an irrational number and equal to $0.7071067812\ldots$ in decimal form. Make the expressionnegative because cosecantis negative in the fourth quadrant. It is called "cotangent" in reference to its reciprocal - the tangent function - which can be represented as a line segment tangent to a circle. What is sin 150 degrees? β = α ± 360 * k, where k is a positive integer. 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. at the angles of 0°, 30°, 60°, 90°: - 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 $ The easiest way to remember the basic values of sin and cos The unit circle has a radius as 1 unit and it is drawn on an XY plane. 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. Math tutorial for using the sum of two angles formula of sine for 105 degrees - Duration: 6:44. Our cotangent calculator accepts input in degrees or radians, so once you have your angle measurement, just type it in and press "calculate". Our cotangent calculator accepts input in degrees or radians, so once you have your angle measurement, just type it in and press "calculate". Find the Exact Value cot(330 degrees ) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Find the Exact Value csc(300 degrees ) Apply the reference angleby finding the anglewith equivalenttrig values in the first quadrant. The result can be shown in multiple forms. 1. The cotangent function is used in the ASA triangle rule (angle-side-angle). Brian McLogan 5,644 views 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°, Sum and Difference of Trigonometric Functions, Multiplication of 2 Trigonometric Functions. 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 range of the function is [-1,1]. 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. Hyp/Adj = Secant. The period of sin is 2$\pi$. Start studying Unit Circle - Degrees. All trigonometric functions are periodic. It is useful for finding an angle x when cot(x) is known. 300 degrees is in the fourth quadrant. How do you use the reference angles to find #sin210cos330-tan 135#? Cos 30° = √3/2 is an irrational number and equals to 0.8660254037 (decimal form). A cotangent of an angle α is also equal to the ratio between its cosine and sine, so cotα = cosα / sinα. 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]. b) for angles measured in radians. This means that the x-coordinate is negative and the y-coordinate is negative. A useful feature is that in trigonometry, any two coterminal angles have exactly the same trigonometric values. The cosine is a trigonometric function. Adj/Hyp = Cosine. The result can be shown in multiple forms. What is the sine, cosine, tangent, cotangent, cosecant, and secant of -90 degrees? How do you find the value of #cot 300^@#? Subscribe! 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. Exact Form: Make the expression negative because cotangent is negative in the fourth quadrant. Why an angle is made up of rays and not of lines or line segments? The exact value of is . How do you know if #sin 30 = sin 150#? -√ 3. cot (300) = -√ 3 /3. Therefore, Sin 30 degree equals to the fractional value of 1/ 2. Make the expression negative because cotangent is negative in the fourth quadrant. The range of the function is [-1,1]. Free trigonometry calculator - calculate trignometric equations, prove identities and evaluate functions step-by-step
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