Math Doubts

Sine values

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The trigonometric function sine gives a value for every angle in a right triangle and it is called the sine value. There are many sine values in trigonometric mathematics but five sine values are mostly used in mathematics and they can be used to derive the remaining sine function values.

Table

The special values of sine function for some standard angles are given here with proofs in a tabular form. The following sine chart is really useful in mathematics for studying the trigonometry in advanced level.

Angle $(\theta)$ Sine value $(\sin{\theta})$
Degrees Radian Grades Fraction Decimal Proof
$0^\circ$ $0$ $0^g$ $0$ $0$
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$30^\circ$ $\dfrac{\pi}{6}$ $33\dfrac{1}{3}^g$ $\dfrac{1}{2}$ $0.5$
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$45^\circ$ $\dfrac{\pi}{4}$ $50^g$ $\dfrac{1}{\sqrt{2}}$ $0.7071$
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$60^\circ$ $\dfrac{\pi}{3}$ $66\dfrac{2}{3}^g$ $\dfrac{\sqrt{3}}{2}$ $0.866$
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$90^\circ$ $\dfrac{\pi}{2}$ $100^g$ $1$ $1$
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Chart

The sine values for different angles are listed in the following tabular form.

Angle $(\theta)$ Sine value $(\sin{\theta})$
Degrees Radian Grades Fraction Decimal Proof
$15^\circ$ $\dfrac{\pi}{12}$ $16\small\dfrac{2}{3}^{\normalsize g\,}$ $\dfrac{\sqrt{3}-1}{2\sqrt{2}}$ $0.2588$
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$18^\circ$ $\dfrac{\pi}{10}$ $20^g$ $\dfrac{\sqrt{5}-1}{4}$ $0.309$
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$36^\circ$ $\dfrac{\pi}{5}$ $40^g$ $\dfrac{\sqrt{10-2\sqrt{5}}}{4}$ $0.5878$
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$54^\circ$ $\dfrac{3\pi}{10}$ $60^g$ $\dfrac{\sqrt{5}+1}{4}$ $0.809$
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Ashok Kumar B.E. - Founder of Math Doubts

Ashok Kumar, B.E.

Founder of Math Doubts

A Specialist in Mathematics, Physics, and Engineering with 14 years of experience helping students master complex concepts from basics to advanced levels with clarity and precision.

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