Sin 37 in fraction

• \sin (x)+\sin (\frac • Show More How to solve trigonometric equations step-by-step? • To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for the variable. Use inverse trigonometric functions to find the solutions, and check for extraneous solutions. •

Ok so on doing a whole lot of Geometry Problems, since I am weak at Trigonometry, I am now focused on $2$ main questions :- $1)$ How to calculate the $\sin,\cos,\tan$ of any angle? Some Information :- This site :- $\sin$ of any angle from $1$ to $90^\circ$ , and I found it very interesting. But now the Questions arise :- Can you find the $\sin$, $\cos$ or $\tan$ of any fraction angles, like $39.67$? Can you find the $\sin$, $\cos$ or $\tan$ of recurring fractions like $\frac^\circ$ . I do not have any specific formula to find this, and I am mainly stuck here. I need a formula which shows how this can be done. Can anyone help me? Thank You. $\begingroup$ Given that we have to compute the sine of some angles by the formula for $\sin(nx)$ which is an n-th degree polynomial in $\sin(x)$ (and $\cos(x)$), and that polynomials of degree 5 and above are in general not solvable by radicals (i.e. there exists polynomials of degree 5 or above which is not solvable by radicals), there is almost certainly some fractional angle whose sine couldn't be expressed in fractions and radicals. $\endgroup$ $\begingroup$ I think you should post the specific question you're dealing with. If it's part of another question, also post that, and include your attempts which led up to the recurring fraction. Would be even better if you write down your thoughts as to how to tackle the sine of the recurring fraction. $\endgroup$ $\begingroup$ Although, one may compute $\sin(1^\circ)$ in radical form by th...

\square^ (2\times2) (2\times3) (3\times3) (3\times2) (4\times2) (4\times3) (4\times4) (3\times4) (2\times4) (5\times5) (1\times2) (1\times3) (1\times4) (1\times5) (1\times6) (2\times1) (3\times1) (4\times1) (5\times1) (6\times1) (7\times1) \mathrm +

The Law of Sines The Law of Sines (or Sine Rule) is very useful for solving triangles: a sin A = b sin B = c sin C It works for any triangle: a, b and c are sides. A, B and C are angles. (Side a faces angle A, side b faces angle B and side c faces angle C). And it says that: When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C Sure ... ? Well, let's do the calculations for a triangle I prepared earlier: a sin A = 8 sin(62.2°) = 8 0.885... = 9.04... b sin B = 5 sin(33.5°) = 5 0.552... = 9.06... c sin C = 9 sin(84.3°) = 9 0.995... = 9.04... The answers are almost the same! (They would be exactly the same if we used perfect accuracy). So now you can see that: a sin A = b sin B = c sin C B = 49.6° Sometimes There Are Two Answers ! There is one very tricky thing we have to look out for: Two possible answers. Imagine we know angle A, and sides a and b. We can swing side a to left or right and come up with two possible results (a small triangle and a much wider triangle) Both answers are right! This only happens in the " not between" case, and even then not always, but we have to watch out for it. Just think "could I swing that side the other way to also make a correct answer?" So there are two possible answers for R: 67.1° and 112.9°: Both are possible! Each one has the 39° angle, and sides of 41 and 28. So, always check to see whether the alternative answer makes sense. • ... s...

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle', and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it.

Quick navigation: • • • • The Sine function ( sin(x) ) The sine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the From cos(α) = a/c follows that the sine of any angle is always less than or equal to one. The function takes negative values for angles larger than 180°. Since for a right triangle the longest side is the hypotenuse and it is opposite to the right angle, the sine of a right angle is equal to the ratio of the hypotenuse to itself, thus equal to 1. You can use this sine calculator to verify this. A commonly used law in trigonometry which is trivially derived from the sine definition is the law of sines: The sine function can be extended to any real value based on the length of a certain line segment in a unit circle (circle of radius one, centered at the origin (0,0) of a Cartesian coordinate system. Other definitions express sines as infinite series or as differential equations, meaning a sine can be an arbitrary positive or negative value, or a complex number. Related trigonometric functions The reciprocal of sine is the cosecant: csc(x), sometimes written as cosec(x), which gives the ratio of the length of the hypotenuse to the length of the side opposite to the angle. The inverse of the sine is the arcsine function: asin(x) or arcsin(x). The arcsine function is multivalued, e.g. arcsin(0) = 0 or π, or 2π, and so on. It is useful for finding an angle x when sin(x) is known. How to calculate the sine...

Arcsin Calculator Online arcsin = Calculate × Reset Angle in degrees: ° Angle in radians: rad Calculation: Arcsine definition The arcsin( y) = sin -1( y) = x + 2 kπ For every k = For example, If the sine of 30° is 0.5: sin(30°) = 0.5 Then the arcsine of 0.5 is 30°: arcsin(0.5) = sin -1(0.5) = 30° y x = arcsin(y) degrees radians -1 -90° -π/2 -0.8660254 -60° -π/3 -0.7071068 -45° -π/4 -0.5 -30° -π/6 0 0° 0 0.5 30° π/6 0.7071068 45° π/4 0.8660254 60° π/3 1 90° π/2 See also • • • • • • •

More • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Step 1: Construct the right-angled triangle using the Pythagorean triplets Construct the right-angled triangle â–³ A B C , with ∠A C B = 37 o , ∠A B C = 90 o , ∠B A C = 5 3 o and sides as 3 c m , 4 c m and 5 c m. Step 2: Find the value of given trigonometric function in terms of fraction We know that, sin ⁡ θ = P H , and for angle θ = 37 o , P = 3 and H = 5 . So, sin ⁡ 37 o = 3 5 . Similarly, for angle θ = 53 o , P = 4 and H = 5 . So, sin ⁡ 53 o = 4 5 . Now, for angle θ = 37 o , P = 3 and B = 4 . So, tan ⁡ 37 o = 3 4 . Similarly, for angle θ = 53 o , P = 4 and B = 3 . So, tan ⁡ 53 o = 4 3 Hence, sin ⁡ 37 o = 3 5 , s...

• \sin (x)+\sin (\frac • Show More How to solve trigonometric equations step-by-step? • To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for the variable. Use inverse trigonometric functions to find the solutions, and check for extraneous solutions. •

The Law of Sines The Law of Sines (or Sine Rule) is very useful for solving triangles: a sin A = b sin B = c sin C It works for any triangle: a, b and c are sides. A, B and C are angles. (Side a faces angle A, side b faces angle B and side c faces angle C). And it says that: When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C Sure ... ? Well, let's do the calculations for a triangle I prepared earlier: a sin A = 8 sin(62.2°) = 8 0.885... = 9.04... b sin B = 5 sin(33.5°) = 5 0.552... = 9.06... c sin C = 9 sin(84.3°) = 9 0.995... = 9.04... The answers are almost the same! (They would be exactly the same if we used perfect accuracy). So now you can see that: a sin A = b sin B = c sin C B = 49.6° Sometimes There Are Two Answers ! There is one very tricky thing we have to look out for: Two possible answers. Imagine we know angle A, and sides a and b. We can swing side a to left or right and come up with two possible results (a small triangle and a much wider triangle) Both answers are right! This only happens in the " not between" case, and even then not always, but we have to watch out for it. Just think "could I swing that side the other way to also make a correct answer?" So there are two possible answers for R: 67.1° and 112.9°: Both are possible! Each one has the 39° angle, and sides of 41 and 28. So, always check to see whether the alternative answer makes sense. • ... s...