Sine function, in a right triangle, is defined as “the ratio of the length of the leg opposite the angle to the length of the hypotenuse”.
Refer to the image below to understand the definition of a sine function:
Trigonometric functions are often studied using special angles, 30°, 45°, and 60°.
To find the value of sin 30, we will consider an equilateral triangle divided into halves to get a 30-60-90 right triangle.
Since it is an equilateral triangle, consider the length of the sides is ‘2x’ units. So, when it is divided into halves, the length of the base will be ‘x’ units.
Now, as per the definition of the sine function, sin 30 = x/(2x) = ½.
Similarly, you can find sine 60 and sine 90 using the definition of the sine function and the ‘Pythagoras theorem’.
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