Find the exact value of sin (75°). Give your answer in its simplest form.

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The exact value of sin (75°) is indeed complicated to calculate and searching for the exact answer is troublesome.

But what if you can find it with just a few step procedures? Things get sorted when a complicated equation is divided into two simpler forms and you get the answer easily.

Wondering how? Here is how you can do that. But here’s a pro tip for you. Before moving forward, you must learn the trigno table so that you don’t get stuck just because you don’t know the values.

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So, let us start with the equation first of how you can split a value.

Taking the common formula of sin (A+B)

Here this equals to,

sin (A+B) = sin (A) cos (B) + sin (B) cos (A)

Calculating the value of sin (75°)

With the help of this equation, we will find the value of sin (75°)

sin (75°), this can be split as

sin (75°) = sin (30+45) °

sin (75°) = sin (30°) cos (45°) + sin (45°) cos (30°)

So, here we need a few values. Let us first write them to make it easy calculation,

The exact value of sin (30°) = ½

The exact value of cos (45°) = √2/2

The exact value of cos (30°) = √3/2

The exact value of sin (45°) = √2/2

Putting the values in the main equation, and let us find the final value of sin (75°)

sin (75°) = ½ X 1/√2 + (√3)/2 X √2/2

sin (75°) = 1/ (2√2) + (√3)/ (2√2)

sin (75°) = (1 + √3)/ (2√2)

And let us find it in decimal form

After putting the values, the whole equation will proceed like,

sin (75°) = √2/4 + √6/4

sin (75°) = √2 + √6/4

sin (75°) = 0.96592582

Bottom Line!

The outcome of the sin (75°) is easier to calculate when split into two the same way like a complicated equation does help after splitting into the two parts. Therefore, after splitting, as you have seen the value finding was easier. Follow the same steps to find some more values!

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