Sin 60 Values
In trigonometry, there are three main functions (or ratios) that measure the angles and lengths of a right-angled triangle. The three ratios are sine, cosine, and tangent which are abbreviated as sin, cos, and tan, respectively. Trigonometric ratios have a lot of functions out of which solving a triangle is the most important purpose. To solve a triangle, information about one or more angles or sides of a triangle is needed for which trigonometric ratios come to save the day using sin, cos, and tan. In this article, the sine of angle 60° is explained.
Sine or sin
In a right-angled triangle, one angle is 90°, and the other two when added together equal to the third angle. The most important and prominent angles are 0, 30°, 45°, 60°, and 90°. Sine is defined as the ratio of the perpendicular to the hypotenuse of a right-angled triangle. Therefore, for an angle ∅, sin ∅ will be Perpendicular/Hypotenuse.
Degrees and Radian
A degree is the most important measurement used in the field of trigonometry which is used to find out unknown angles.
Let's take an example of a clock which is a total of 360°. Every quarter of an hour represents 90° and the degree is further divided into minutes and seconds represented by ‘ and ‘ respectively.
The value of angles can also be referred to by radians, denoted by π which is equal to 180°. A radian is considered to be a unit circle that has a radius equal to one. Therefore, a circle has a total of 2π radians.
Values of Angles and Radians
All values of sin, cos, and tan can be found from 0 to 90° which are then repeated for other respective values over 90°. Tan ∅ can be written as sin∅/cos ∅. But now, only the basic and most important values of angles are to be learned first.
Sine:
sin 0 = 0
sin 30° = ½
sin 45°= 1/√2
sin 60°= √3/2
sin 90°= 1
Cosine:
Cos 0° = Sin 90° = 1
Cos 30°= Sin 60° = √3/2
Cos 45° = Sin 45° = 1/√2
Cos 60° = Sin 30° =½
Cos 90° = Sin 0° = 0
Tangent:
Tan 0° = Sin 0°/Cos 0° = 0
Similarly,
Tan 30° =1/√3
Tan 45° = 1
Tan 60° = √3
Tan 90° = ∞
For more information on sin 60° and other values of sin, cos, and tan, visit Vedantu's website and get practice questions, solutions, and more!
FAQs on Sin 60 Degrees
1. What is the need for a sin ratio?
In a situation where the perpendicular and hypotenuse of a right-angled triangle are known and the base has to be found out, the sine ratio formula is used. When the angle between hypotenuse and base is known, the value of sine can also be found out using that angle.
2. What is the value of sin 60°?
The value of sin 60° is √3/2 which is the same as the value of cos 30°.
3. Where can I get practice questions on sin, cos, and tan?
You can get practice questions, solutions for NCERT, and other book exercise questions on trigonometric ratios of sin, cos, tan, and others on Vedantu's website and app. You can download them for free and use them as you need anytime, anywhere! They are downloadable in PDF format which means you can have access even without an internet connection. Use these resources to your advantage and start your preparation now!