What is the exact value of cot(5pi/6)?
If you draw the angle, then draw a line down to the x axis, you will find that your reference angle is pi/6.
tan(pi/6) should be a memory value; cot is its reciprocal. Remember that your angle is in Quadrant II.
I'm sorry, I'm still confused :s
I cannot post images here - you'll have to draw it yourself.
1. Draw the units circle, then draw the angle 5pi/6.
2. draw a line from that angle to the x axis
3. The angle of the resulting triangle is your reference angle.
Can you get that far?
To find the exact value of cot(5π/6), we can use the unit circle. The cotangent (cotθ) of an angle is defined as the ratio of the adjacent side to the opposite side of a right triangle formed by that angle.
In the case of cot(5π/6), we should first identify the reference angle. The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis on the unit circle.
For 5π/6, the reference angle is π/6 since it is the acute angle formed by the terminal side of 5π/6 and the x-axis.
Next, we need to determine the sign of the cotangent based on the quadrant in which the original angle lies. Since 5π/6 is in the second quadrant, where the x-coordinate is negative, the cotangent will be negative.
Now, let's find the value of cot(π/6) on the unit circle. Considering the reference angle π/6, we can see that on the unit circle, the x-coordinate of the point corresponding to π/6 is (√3)/2, and the y-coordinate is 1/2.
Therefore, cot(π/6) = adjacent side / opposite side = (√3)/2 / (1/2) = √3.
Since we have determined that cot(5π/6) is negative, the exact value is -√3.