Evaluate each expression.cot(11π6)\cot\left(\frac{11\pi}{6}\right)cot(611π)

− 3 -\sqrt3 − 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

Evaluate each expression. cot ( 11 π 6 ) \cot\left(\frac{11\pi}{6}\right) cot ( 6 11 π )

this problem, we're asked to evaluate the expression and the expression we're given here is the cotangent of 11 pi over six. Now remember the cotangent is just the reciprocal of tangent and on the unit circle I know that the tangent is just y over x. So that means that the cotangent is just that flipped x over y. So I can locate this angle on my unit circle and divide those values accordingly. So on my unit circle I see that 11 pi over six is right down here in quadrant four and I have my x and my y values. Now when dividing these remember that when we have the same denominator we're effectively just dividing those numerators. So here in order to do that I'm taking my numerator of my x value dividing it by my numerator of my y value to give me the square root of three over negative negative one. Now dividing that out just gives me the negative square root of three and I'm done here. The cotangent of 11 pi over six is negative square root of three. Thanks for watching and let me know if you have any questions.

Evaluate each expression. cot ⁡ ( 11 π 6 ) \cot\left(\frac{11\pi}{6}\right) cot ( 6 11 π )

− 3 -\sqrt3 − 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

− 3 3 -\frac{\sqrt3}{3} − 3 3 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

12. Trigonometric Functions

Trigonometric Functions on the Unit Circle

Business Calculus

12. Trigonometric Functions

Trigonometric Functions on the Unit Circle

Struggling with Business Calculus?

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Multiple Choice

Evaluate each expression.
$\cot\left(\frac{11\pi}{6}\right)$

$\frac12$

$-\frac{\sqrt3}{3}$

$-\sqrt3$

$2$

Verified step by step guidance

Step 1: Recall the definition of cotangent. The cotangent function is defined as cot(θ) = cos(θ) / sin(θ). To evaluate cot(11π/6), we need to find the cosine and sine of 11π/6.

Step 2: Determine the reference angle and quadrant. The angle 11π/6 is in the fourth quadrant, and its reference angle is π/6. In the fourth quadrant, cosine is positive, and sine is negative.

Step 3: Use the unit circle values for π/6. From the unit circle, cos(π/6) = √3/2 and sin(π/6) = 1/2. Since 11π/6 is in the fourth quadrant, cos(11π/6) = √3/2 and sin(11π/6) = -1/2.

Step 4: Substitute the values of cosine and sine into the cotangent formula. cot(11π/6) = cos(11π/6) / sin(11π/6) = (√3/2) / (-1/2).

Step 5: Simplify the expression. Dividing (√3/2) by (-1/2) is equivalent to multiplying √3/2 by -2/1, which simplifies to -√3.

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