What is the value of sin 45 but as a fraction?

Question

asked Oct 12, 2024 157k views

2 Answers

Noam Solovechick · Answer 1 · 2024-10-14T14:54:07+0000

Answer: 1 divided by the square root of 2

Explanation:

Let's set up an example, if the angle is forty five degrees, and the opposite length is 1, we can solve this as sin to get to the hypotenuse,

1. sin(45) = 1/hyp

2. sin(45) times hyp = 1

3. hyp = sin(45)/1

If we take any answer and put it over the hypotenuse as sin, we can see that it is going to end up as 1/√2, or 0.707

I did 1 because you are just asking for sin(45).

Mkon · Answer 2 · 2024-10-17T13:29:12+0000

The exact value of sin 45° is
(√(2) )/(2)

Since we have given that

$\text{sin} \ 45^\circ$

We need to find the exact value of sin 45°.

From the trigonometric table,

$\text{sin} \ 45^\circ=(1)/(√(2))$

We need to write it as a simplified fraction,

So, for this, we will rationalize the denominator:

(1)/(√(2))*(√(2) )/(√(2))

=(√(2) )/(2)

Hence, the exact value of sin 45° is
(√(2) )/(2)