Question

Sin(25pi/2)

Answer 1

I am looking for the exact value of the Trigonometric function Sin (25Pi/2)

Answer 2

\(\bf \large \frac{25}{2} \implies 12\frac{1}{2} \implies (2 \times 6)\frac{1}{2}\implies (2\pi \times 6)\frac{1}{2}\)

Answer 3

so that'd be \(\bf 2\pi\) 6 times, that is, the angle going around cyclically 6 times
and then you add 1/2 more
so \(\bf \cfrac{25\pi}{2}\) is a coterminal angle with \(\cfrac{\pi}{2}\) and it's sine will be the same for both
so what's the \(\bf sin\left(\cfrac{\pi}{2}\right)\) ?

Answer 4

Remember that Sine is a periodic function and 2π is one full revolution...meaning you can add or subtract 2π (or any integral multiple of it) from an argument without changing the value of its sine.

Try subtracting, since your argument is larger than 2π:

25π/6 - 2π
25π/6 - 12π/6
13π/6

That's still larger than 2π, so do it again:
13π/6 - 12π/6
π/6

sin(25π/6) = sin(13π/6) = sin(π/6) = ½

Answer 5

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