Sin 45 Degrees

In trigonometry, there are three primary ratios, Sine, Cosine and Tangent, which are used to find the angles and length of the right-angled triangle. Before discussing Sin 45 degrees, let us know the importance of Sine function in trigonometry. Sine function defines a relation between the acute angle of a right-angled triangle and the opposite side to the angle and hypotenuse. Or you can say, the Sine of angle α is equal to the ratio of the opposite side(perpendicular) and hypotenuse of a right-angled triangle.

The trigonometry ratios sine, cosine and tangent for an angle α are the primary functions. The value for sin 45 degrees and other trigonometry ratios for all the degrees 00, 300, 600, 900,1800 are generally used in trigonometry equations. These values are easy to remember with the help trigonometry table, which will also be provided in this article.

Let us discuss first discuss sin 45 degrees value, here in this article.

Sin 45 Degree Value

Let us consider a right-angled triangle △ABC. Thus, the sine of angle α is a ratio of the length of the opposite side,BC to the angle α and its hypotenuse AB.

Sin 45 degrees

Sin α = \(\frac{Opposite Side}{Hypotenuse}\)

= \(\frac{Perpendicular}{Hypotenuse}\)


So, sin 45 degrees trigonometry value, in-fraction will be, sin 450 = \(\frac{Perpendicular}{Hypotenuse}\)

A simple method by means of which we can calculate the value of sine ratios for all the degrees is discussed here. After learning this method, you can easily calculate the values for all other trigonometry ratios. So, let’s start to calculate the value for sin 45 degrees table of trigonometry.

Sin 00 = \(\sqrt{0/4}\) = 0

Sin 300 = \(\sqrt{1/4}\) = ½

Sin 450 = \(\sqrt{2/4}\) = \(1/\sqrt{2}\)

Sin 600 = \(\sqrt{3/4}\) = \(\sqrt{3}/2\)

Sin 900 = \(\sqrt{4/4}\) = 1

Therefore, Sine ratio table for both degrees and radians can be written as;

Sine 00 0
Sine 300 or Sine π/6 1/2
Sine 450 or Sine π/4 \(1/\sqrt{2}\)
Sine 600 or Sine π/3 \(\sqrt{3}/2\)
Sine 900 or Sine π/2 1
Sine 1200 or Sine 2π/3 \(\sqrt{3}/2\)
Sine 1500 or Sine 5π/6 1/2
Sine 1800 or Sine π 0
Sine 2700 or Sine 3π/2 -1
Sine 3600 or Sine 2π 0

In the same way, we can find the values for other trigonometry ratios such as cosine and tangent. Here we are providing you the table for sine, cosine and tangent ratios.

Degrees 0 30 45 60 90 180 270 360
Sin 0 1/2 \(1/\sqrt{2}\) \(\sqrt{3}/2\) 1 0 -1 0
Cos 1 \(\sqrt{3}/2\) \(1/\sqrt{2}\) 1/2 0 -1 0 1
Tan 0 1/\(\sqrt{3}\) 1 \(\sqrt{3}\) 0 0

sin 45 degrees value

Learn more about trigonometric ratios and formulas and identities and download BYJU’S-The Learning App for a better experience.


Practise This Question

The curved surface of a  cylindrical bulb of height 18cm and base radius 7 cm is to be painted in  luminating gold colour such that 2/3 rd of the height of bulb emits golden  light, painting is done at Rs. 5 per sq. cm. The cost of painting the bulb is   (pi =227)