What is the exact value of: sin 29pi/6
To find the exact value of sin(29π/6), we can first find the reference angle of 29π/6.
The reference angle is the positive acute angle between the terminal side of the angle and the x-axis.
To find the reference angle, we can subtract multiples of 2π from 29π/6 until we obtain an angle between 0 and 2π.
29π/6 - 12π = π/6
Therefore, the reference angle for 29π/6 is π/6.
Now, we can determine the sign of sin(29π/6) based on the quadrant where the angle lies.
Since the given angle is greater than 2π (full revolution) but less than 3π/2 (270 degrees), it lies in the third quadrant. In the third quadrant, the sine function is negative.
So, sin(29π/6) is negative.
Lastly, we need to determine the value of sin(π/6), which is the same as sin(30 degrees).
The exact value of sin(30 degrees) is 1/2.
Therefore, the exact value of sin(29π/6) is -1/2.
To find the exact value of sin(29π/6), we can use the unit circle.
1. Start by understanding the angle measure: 29π/6. This fraction tells us that the angle is 29 times the reference angle π/6.
2. Recall that the unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. The reference angle π/6 represents an angle of 30 degrees (or π/6 radians) measured counterclockwise from the positive x-axis.
3. To find the value of sin(29π/6), we need to determine the angle that is equivalent to 29π/6. Start with the reference angle π/6 and find its equivalent angles.
a. Since the π/6 reference angle measures 30 degrees, we can add multiples of 360 degrees to get equivalent angles.
π/6 + 360° = 390°
π/6 + 2 * 360° = 750°
π/6 + 3 * 360° = 1110°
b. We continue this process until we get an angle equivalent to 29π/6:
π/6 + 14 * 360° = 5220°
4. Now, we need to convert 5220° to the equivalent radians. Since 180° = π radians, we can multiply 5220° by π/180° to get the measurement in radians.
5220° * (π/180°) = 29π/6
5. Finally, we can find the exact value of sin(29π/6). Because angles that differ by a multiple of 2π (360°) have the same sine value, sin(29π/6) will have the same value as sin(π/6).
The exact value of sin(π/6) is 1/2.
Therefore, the exact value of sin(29π/6) is 1/2.
29*180/6 = 870o = 150o CCW.
sin150 = sin30 = 1/2.
c'mon, guy. This is just like the earlier one
29pi/6 = 4pi + 5pi/6
sin 5pi/6 = sin (pi-pi/6) = sin pi/6 = 1/2