wha tis the exact value of sin 9pi/4
To find the value of sin(9π/4), we need to first determine the angle in the standard position that is coterminal with 9π/4.
To do this, we can use the fact that adding or subtracting a full revolution (2π) to an angle in the standard position does not change its trigonometric function values.
So, we can add or subtract 2π until we get an angle between 0 and 2π.
9π/4 = (8π/4) + (π/4) = 2π + π/4
Now we can see that sin(9π/4) is equal to sin(π/4) because they are coterminal angles.
The value of sin(π/4) is (√2)/2.
Therefore, the exact value of sin(9π/4) is (√2)/2.
To find the exact value of sin(9π/4), we can use the unit circle and the properties of the sine function.
1. Start by drawing a unit circle, which is a circle with a radius of 1 unit.
2. Divide the circle into four quadrants, labeling them as follows:
- Quadrant I: 0 ≤ θ < π/2
- Quadrant II: π/2 ≤ θ < π
- Quadrant III: π ≤ θ < 3π/2
- Quadrant IV: 3π/2 ≤ θ < 2π
3. Express 9π/4 as an angle in terms of π. Since 9π/4 is greater than 2π (a full circle), we can subtract 2π until we get an angle between 0 and 2π.
9π/4 - 2π = π/4
4. Determine the quadrant in which π/4 lies. In this case, π/4 lies in Quadrant I.
5. Recall that the sine of an angle is the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
In Quadrant I, the y-coordinate of the point on the unit circle is positive.
6. Find the exact value of sin(π/4). In the case of π/4, it corresponds to a 45-degree angle. This angle forms a right triangle in Quadrant I, where the opposite side is √2 and the hypotenuse is 1 (since we are using a unit circle).
sin(π/4) = opposite/hypotenuse = √2/1 = √2
Therefore, the exact value of sin(9π/4) is √2.
add Subract 2PI
sin (9pi/4)==sin(9PI/4-8PI/4)=sin(Pi/4)
which you should have memorized as 1/2 sqrt2