Sin 45 value in trigonometry table

When I was first introduced to trigonometric ratios, I learned the following trick to remember the $0^$. Of course it's not just coincidence. The angles $0^\circ,$ $30^\circ,$ $45^\circ,$ $60^\circ,$ and $90^\circ$ are "standard angles" precisely because they are easy to express as exact numbers of degrees and they have relatively simple expressions for sine and cosine compared to other such angles. The angle $30^\circ$ is nice because it is one of the angles of the right triangles that you get when you cut an equilateral triangle into two right triangles. Half of one side of the equilateral triangle becomes a leg of a right triangle and another side becomes the hypotenuse, and as a result it's easy to see that $\sin(30^\circ) = \frac12.$ The square root part of the trick comes from the Pythagorean Theorem. If one acute angle of a triangle is $\theta,$ the other angle is $90^\circ - \theta,$ and it follows that $$ (\sin(\theta))^2 + (\sin(90^\circ - \theta))^2 = 1. $$ Let $\theta = 45^\circ,$ and then $90^\circ - \theta$ is also $45^\circ$, so $(\sin(\theta))^2$ added to itself is $1.$ It follows that $(\sin(45^\circ))^2 = \frac12.$ Let $\theta = 30^\circ$; we already found that $\sin(30^\circ) = \frac12,$ so $(\sin(30^\circ))^2 = \frac14.$ But then $90^\circ - \theta$ is $60^\circ,$ so $(\sin(30^\circ))^2 + (\sin(60^\circ))^2 = 1.$ That implies that $(\sin(60^\circ))^2 = \frac34.$ Obviously $\sin(0^\circ) = 0$ and $\sin(90^\circ) = 1.$ So now we have found five simple-to-...

Sine The sine of an angle is a trigonometric function that is denoted by sin x, where x is the angle in consideration. In a right-angled triangle, the ratio of the perpendicular and the hypotenuse is called the sine function. In other words, it is the ratio of the side opposite to the angle in consideration and the hypotenuse and its value vary as the angle varies. The sine function is used to represent sound and light waves in the field of physics. In this article, we will learn the basic properties of sin x, sine graph, its domain and range, derivative, integral, and power series expansion. The sine function is a periodic function and has a period of 2π. We will solve a few examples using the sine function for a better understanding of the concept. 1. 2. 3. 4. 5. 6. 7. 8. 9. What Is Sine? The sine of an angle in a right-angled triangle is a ratio of the side opposite to an angle and the hypotenuse. The sine function is an important Hence, the sine function for the above case can be mathematically written as sin x = PQ/OP. Here, x is the acute angle between the hypotenuse and the base of a right-angled triangle OPQ. Sine Function Domain and Range The domain of sine function is all real numbers as sin x is defined for all x in (-∞, ∞). Whereas the range of sin x is [-1, 1] as the value of sin x does not go beyond this. The graph of sine function looks like a wave that oscillates between -1 and 1. Also, the period of sin x is 2π as its value repeats after every 2π radians. ...

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Sine Tables Chart of the angle 0° to 90° An online trigonometric tables 0° to 15° 16° to 31° 32° to 45° sin(0°) = 0 sin(16°) = 0.275637 sin(32°) = 0.529919 sin(1°) = 0.017452 sin(17°) = 0.292372 sin(33°) = 0.544639 sin(2°) = 0.034899 sin(18°) = 0.309017 sin(34°) = 0.559193 sin(3°) = 0.052336 sin(19°) = 0.325568 sin(35°) = 0.573576 sin(4°) = 0.069756 sin(20°) = 0.34202 sin(36°) = 0.587785 sin(5°) = 0.087156 sin(21°) = 0.358368 sin(37°) = 0.601815 sin(6°) = 0.104528 sin(22°) = 0.374607 sin(38°) = 0.615661 sin(7°) = 0.121869 sin(23°) = 0.390731 sin(39°) = 0.62932 sin(8°) = 0.139173 sin(24°) = 0.406737 sin(40°) = 0.642788 sin(9°) = 0.156434 sin(25°) = 0.422618 sin(41°) = 0.656059 sin(10°) = 0.173648 sin(26°) = 0.438371 sin(42°) = 0.669131 sin(11°) = 0.190809 sin(27°) = 0.45399 sin(43°) = 0.681998 sin(12°) = 0.207912 sin(28°) = 0.469472 sin(44°) = 0.694658 sin(13°) = 0.224951 sin(29°) = 0.48481 sin(45°) = 0.707107 sin(14°) = 0.241922 sin(30°) = 0.5 sin(15°) = 0.258819 sin(31°) = 0.515038 46° to 60° 61° to 75° 76° to 90° sin(46°) = 0.71934 sin(61°) = 0.87462 sin(76°) = 0.970296 sin(47°) = 0.731354 sin(62°) = 0.882948 sin(77°) = 0.97437 sin(48°) = 0.743145 sin(63°) = 0.891007 sin(78°) = 0.978148 sin(49°) = 0.75471 sin(64°) = 0.898794 sin(79°) = 0.981627 sin(50°) = 0.766044 sin(65°) = 0.906308 sin(80°) = 0.984808 sin(51°) = 0.777146 sin(66°) = 0.913545 sin(81°) = 0.987688 sin(52°) = 0.788011 sin(67°) = 0.920505 sin(82°) = 0.990268 sin(53°) = 0.798636 sin(68°) = 0.927184 sin(83°) =...

Trigonometry Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a  right-angled triangle. This concept is given by the Greek mathematician Hipparchus. In this article, we are going to learn the basics of trigonometry such as trigonometry functions, ratios, trigonometry table, formulas and many solved examples. Table of contents: • • • • • • • • • • • • • • • What is Trigonometry? Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle. Hence, it helps to find the missing or unknown angles or sides of a right triangle using the trigonometric formulas, functions or trigonometric identities. In trigonometry, the angles can be either measured in degrees or radians. Some of the most commonly used trigonometric angles for calculations are 0°, 30°, 45°, 60° and 90°. Trigonometry is further classified into two sub-branches. The two different types of trigonometry are: • Plane Trigonometry • Spherical Trigonometry In this article, let us discuss the six important trigonometric functions, ratios, trigonometry table, formulas and identities which helps to find the missing angles or sides of a right triangle. Trigonometry Ratios-Sine, Cosine, Tangent The trigonometric ratios o...

Trigonometry Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a  right-angled triangle. This concept is given by the Greek mathematician Hipparchus. In this article, we are going to learn the basics of trigonometry such as trigonometry functions, ratios, trigonometry table, formulas and many solved examples. Table of contents: • • • • • • • • • • • • • • • What is Trigonometry? Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle. Hence, it helps to find the missing or unknown angles or sides of a right triangle using the trigonometric formulas, functions or trigonometric identities. In trigonometry, the angles can be either measured in degrees or radians. Some of the most commonly used trigonometric angles for calculations are 0°, 30°, 45°, 60° and 90°. Trigonometry is further classified into two sub-branches. The two different types of trigonometry are: • Plane Trigonometry • Spherical Trigonometry In this article, let us discuss the six important trigonometric functions, ratios, trigonometry table, formulas and identities which helps to find the missing angles or sides of a right triangle. Trigonometry Ratios-Sine, Cosine, Tangent The trigonometric ratios o...

Sine The sine of an angle is a trigonometric function that is denoted by sin x, where x is the angle in consideration. In a right-angled triangle, the ratio of the perpendicular and the hypotenuse is called the sine function. In other words, it is the ratio of the side opposite to the angle in consideration and the hypotenuse and its value vary as the angle varies. The sine function is used to represent sound and light waves in the field of physics. In this article, we will learn the basic properties of sin x, sine graph, its domain and range, derivative, integral, and power series expansion. The sine function is a periodic function and has a period of 2π. We will solve a few examples using the sine function for a better understanding of the concept. 1. 2. 3. 4. 5. 6. 7. 8. 9. What Is Sine? The sine of an angle in a right-angled triangle is a ratio of the side opposite to an angle and the hypotenuse. The sine function is an important Hence, the sine function for the above case can be mathematically written as sin x = PQ/OP. Here, x is the acute angle between the hypotenuse and the base of a right-angled triangle OPQ. Sine Function Domain and Range The domain of sine function is all real numbers as sin x is defined for all x in (-∞, ∞). Whereas the range of sin x is [-1, 1] as the value of sin x does not go beyond this. The graph of sine function looks like a wave that oscillates between -1 and 1. Also, the period of sin x is 2π as its value repeats after every 2π radians. ...

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Sine Tables Chart of the angle 0° to 90° An online trigonometric tables 0° to 15° 16° to 31° 32° to 45° sin(0°) = 0 sin(16°) = 0.275637 sin(32°) = 0.529919 sin(1°) = 0.017452 sin(17°) = 0.292372 sin(33°) = 0.544639 sin(2°) = 0.034899 sin(18°) = 0.309017 sin(34°) = 0.559193 sin(3°) = 0.052336 sin(19°) = 0.325568 sin(35°) = 0.573576 sin(4°) = 0.069756 sin(20°) = 0.34202 sin(36°) = 0.587785 sin(5°) = 0.087156 sin(21°) = 0.358368 sin(37°) = 0.601815 sin(6°) = 0.104528 sin(22°) = 0.374607 sin(38°) = 0.615661 sin(7°) = 0.121869 sin(23°) = 0.390731 sin(39°) = 0.62932 sin(8°) = 0.139173 sin(24°) = 0.406737 sin(40°) = 0.642788 sin(9°) = 0.156434 sin(25°) = 0.422618 sin(41°) = 0.656059 sin(10°) = 0.173648 sin(26°) = 0.438371 sin(42°) = 0.669131 sin(11°) = 0.190809 sin(27°) = 0.45399 sin(43°) = 0.681998 sin(12°) = 0.207912 sin(28°) = 0.469472 sin(44°) = 0.694658 sin(13°) = 0.224951 sin(29°) = 0.48481 sin(45°) = 0.707107 sin(14°) = 0.241922 sin(30°) = 0.5 sin(15°) = 0.258819 sin(31°) = 0.515038 46° to 60° 61° to 75° 76° to 90° sin(46°) = 0.71934 sin(61°) = 0.87462 sin(76°) = 0.970296 sin(47°) = 0.731354 sin(62°) = 0.882948 sin(77°) = 0.97437 sin(48°) = 0.743145 sin(63°) = 0.891007 sin(78°) = 0.978148 sin(49°) = 0.75471 sin(64°) = 0.898794 sin(79°) = 0.981627 sin(50°) = 0.766044 sin(65°) = 0.906308 sin(80°) = 0.984808 sin(51°) = 0.777146 sin(66°) = 0.913545 sin(81°) = 0.987688 sin(52°) = 0.788011 sin(67°) = 0.920505 sin(82°) = 0.990268 sin(53°) = 0.798636 sin(68°) = 0.927184 sin(83°) =...

When I was first introduced to trigonometric ratios, I learned the following trick to remember the $0^$. Of course it's not just coincidence. The angles $0^\circ,$ $30^\circ,$ $45^\circ,$ $60^\circ,$ and $90^\circ$ are "standard angles" precisely because they are easy to express as exact numbers of degrees and they have relatively simple expressions for sine and cosine compared to other such angles. The angle $30^\circ$ is nice because it is one of the angles of the right triangles that you get when you cut an equilateral triangle into two right triangles. Half of one side of the equilateral triangle becomes a leg of a right triangle and another side becomes the hypotenuse, and as a result it's easy to see that $\sin(30^\circ) = \frac12.$ The square root part of the trick comes from the Pythagorean Theorem. If one acute angle of a triangle is $\theta,$ the other angle is $90^\circ - \theta,$ and it follows that $$ (\sin(\theta))^2 + (\sin(90^\circ - \theta))^2 = 1. $$ Let $\theta = 45^\circ,$ and then $90^\circ - \theta$ is also $45^\circ$, so $(\sin(\theta))^2$ added to itself is $1.$ It follows that $(\sin(45^\circ))^2 = \frac12.$ Let $\theta = 30^\circ$; we already found that $\sin(30^\circ) = \frac12,$ so $(\sin(30^\circ))^2 = \frac14.$ But then $90^\circ - \theta$ is $60^\circ,$ so $(\sin(30^\circ))^2 + (\sin(60^\circ))^2 = 1.$ That implies that $(\sin(60^\circ))^2 = \frac34.$ Obviously $\sin(0^\circ) = 0$ and $\sin(90^\circ) = 1.$ So now we have found five simple-to-...