Find the Value of sin75°

Q. Find the value of sin 75°.

Trigonometry could be defined as a discipline of mathematics which focuses on the interaction between both the proportions of a right-angled triangle’s sides as well as its angles.

To find the value of Sin 75°, a step by step approach needs to be followed and further we need to revisit some concepts and values from Trigonometry.

Explanation of process:

Sin 75° can be written as,

⇒ Sin 75° = Sin (45° + 30°) …… (1)

Now, as we knowledge of the following Trigonometric formulas:

⇒ Sin (A + B) = Sin A. Cos B + Cos A. Sin B

Applying this formula, (1) could be written as:

Assuming A = 45 & B = 30

⇒ Sin (45 + 30) = Sin 45. Cos 30 + Cos 45. Sin 30 …….. (2)

Now, revisiting some values of sin and cos from Trigonometric Table:

Sin Values from the Trigonometric Table from 0 to 90 degrees are as follows

Cos Values from the Trigonometric Table from 0 to 90 degrees are as follows

Now applying the above mentioned trigonometric values in (2), we get

Now revisiting (1), this implies