how do i find the exact value of s

[pie/2, pie]
sin s = radical2/ whole number 2

what is s in radians?

how do i figure this out without the use of a calculator. I drew the graph and located it in the second quadrant and i think the triangle is a 45-45-90 but i don't how to find the radians for the sin of s.

start with this equation:

π radians = 180°
now divide this by simple whole numbers
e.g.
divide by 2 ---> π/2 = 90°
divide by 3 ---> π/3 = 60°
divide by 4 ---> π/4 = 45°
divide by 5 ---> π/5 = 36
divide by 6 ---> π/6 = 30°
divide by 8 ---> π/8 = 22.5°
etc.
copy this chart into a handy place in your notebook.

you know that the sine is positive in the first and 2nd quadrant.
Since s of sin s in in the second quadrant,
s = π - π/4 = 3π/4 , (180-45 = 135°)

check:
sin 3π/4 = .707106781... = √2/2

To find the exact value of s in radians without using a calculator, we can use the relationship between the sine function and the special right triangle with angles of 45 degrees.

First, let's consider the given equation sin(s) = √2/2. This tells us that the sine of s is equal to the square root of 2 divided by 2.

Since we know that the special right triangle with angles of 45 degrees is a 45-45-90 triangle, we can conclude that the opposite and adjacent sides of the triangle are equal.

Let's use the unit circle to help us determine the reference angle. The unit circle is a circle with a radius of 1, and it represents all possible values of sine and cosine functions.

In this case, the reference angle for s will be found in the second quadrant, where sine is positive and cosine is negative.

Since the reference angle for a 45-degree angle is π/4 radians, we can conclude that the reference angle for s is also π/4 radians.

To determine the value of s, we need to consider the unit circle and the position of the angle in the second quadrant. Since we have a 45-45-90 triangle, both legs are equal, and the length of each leg will be 1 / √2.

Since s is in the second quadrant, the angle is greater than π/2 but less than π radians. Therefore, s is in the range [π/2, π].

In conclusion, the exact value of s in radians is π/4 + π/2, which simplifies to 3π/4.