`color {green}{★ ul"Introduction"}`
`\color{green} ✍️` The word `"‘trigonometry’"` is derived from the Greek words `color{green}{"‘trigon’"}` and `color{green}{"‘metron’"}` and it means `color{green}{"‘measuring the sides of a triangle’."}`
`color {green}{★ ul"Angles "}`
`\color{green} ✍️` Angle is a measure of rotation of a given ray about its initial point.
`\color{green} ✍️` The original ray is called `color{blue}{ul"the initial side"}` and the final position of the ray after rotation is called `color{blue}{ul"the terminal side of the angle .")`
`\color{green} ✍️` The point of rotation is called `color{blue}{ul"the vertex."}`
`color {green}{★ ul"One Degree "}`
If a rotation from the initial side to terminal side is `(1/360)^(th)` of a revolution, the angle is said to have a measure of `color{blue}{ul"one degree"}`, written as `1°.`
A degree is divided into `60` minutes, and a minute is divided into `60` seconds.
`color {green}{★ ul"A Minute "}`
● One sixtieth of a degree is called `color{blue}{ul"a minute"}`, written as `1′`.
`color {green}{★ ul"A Second "}`
● one sixtieth of a minute is called `color{blue}{ul"a second"}`, written as `1″.`
Thus, ` \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{green} (1° = 60′, \ \ \ \ \ \ \1′ = 60″)`
`color {green}{★ ul"1 radian"}`
Angle subtended at the centre by an arc of length `1` unit in a unit circle (circle of radius `1` unit) is said to have a measure of `color{green}(ul"1 radian")`.
● We know that the circumference of a circle of radius `1` unit is `2π.` Thus, one complete revolution of the initial side subtends an angle of `2π` radian.
`color {green}{★ ul"Introduction"}`
`\color{green} ✍️` The word `"‘trigonometry’"` is derived from the Greek words `color{green}{"‘trigon’"}` and `color{green}{"‘metron’"}` and it means `color{green}{"‘measuring the sides of a triangle’."}`
`color {green}{★ ul"Angles "}`
`\color{green} ✍️` Angle is a measure of rotation of a given ray about its initial point.
`\color{green} ✍️` The original ray is called `color{blue}{ul"the initial side"}` and the final position of the ray after rotation is called `color{blue}{ul"the terminal side of the angle .")`
`\color{green} ✍️` The point of rotation is called `color{blue}{ul"the vertex."}`
`color {green}{★ ul"One Degree "}`
If a rotation from the initial side to terminal side is `(1/360)^(th)` of a revolution, the angle is said to have a measure of `color{blue}{ul"one degree"}`, written as `1°.`
A degree is divided into `60` minutes, and a minute is divided into `60` seconds.
`color {green}{★ ul"A Minute "}`
● One sixtieth of a degree is called `color{blue}{ul"a minute"}`, written as `1′`.
`color {green}{★ ul"A Second "}`
● one sixtieth of a minute is called `color{blue}{ul"a second"}`, written as `1″.`
Thus, ` \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{green} (1° = 60′, \ \ \ \ \ \ \1′ = 60″)`
`color {green}{★ ul"1 radian"}`
Angle subtended at the centre by an arc of length `1` unit in a unit circle (circle of radius `1` unit) is said to have a measure of `color{green}(ul"1 radian")`.
● We know that the circumference of a circle of radius `1` unit is `2π.` Thus, one complete revolution of the initial side subtends an angle of `2π` radian.