Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find tan((pi)/(12)) exactly using an angle addition or subtraction formula. [Hint: This diagram of special trigonometry. values may help.] Choose 1 answer: (A) (3-sqrt3)/(3+sqrt3) (B) (-3-sqrt3)/(3-sqrt3) (C) (3+sqrt3)/(3-sqrt3) (D) (-3+sqrt3)/(3+sqrt3)

Find tan⁡(π12) \tan \left(\frac{\pi}{12}\right) exactly using an angle addition or subtraction formula.\newline[Hint: This diagram of special trigonometry. values may help].\newlineChoose 11 answer:\newline(A) 3−33+3 \frac{3-\sqrt{3}}{3+\sqrt{3}} \newline(B) −3−33−3 \frac{-3-\sqrt{3}}{3-\sqrt{3}} \newline(C) 3+33−3 \frac{3+\sqrt{3}}{3-\sqrt{3}} \newline(D) −3+33+3 \frac{-3+\sqrt{3}}{3+\sqrt{3}}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Domain and rangeright chevron icon

Full solution

Q. Find tan⁡(π12) \tan \left(\frac{\pi}{12}\right) exactly using an angle addition or subtraction formula.\newline[Hint: This diagram of special trigonometry. values may help].\newlineChoose 11 answer:\newline(A) 3−33+3 \frac{3-\sqrt{3}}{3+\sqrt{3}} \newline(B) −3−33−3 \frac{-3-\sqrt{3}}{3-\sqrt{3}} \newline(C) 3+33−3 \frac{3+\sqrt{3}}{3-\sqrt{3}} \newline(D) −3+33+3 \frac{-3+\sqrt{3}}{3+\sqrt{3}}
  1. Recognize the angle: Recognize that (π)/12(\pi)/12 is not a standard angle for which we have a direct trigonometric value. However, we can express (π)/12(\pi)/12 as the difference of two angles whose tangent values we know: (π)/12=(π)/4−(π)/6(\pi)/12 = (\pi)/4 - (\pi)/6.
  2. Use the tangent subtraction formula: Use the tangent subtraction formula: tan⁡(A−B)=tan⁡(A)−tan⁡(B)1+tan⁡(A)tan⁡(B)\tan(A - B) = \frac{\tan(A) - \tan(B)}{1 + \tan(A)\tan(B)}. Here, A=π4A = \frac{\pi}{4} and B=π6B = \frac{\pi}{6}.
  3. Find tangent values: Find the tangent values for AA and BB. We know that tan⁡(π4)=1\tan(\frac{\pi}{4}) = 1 and tan⁡(π6)=33\tan(\frac{\pi}{6}) = \frac{\sqrt{3}}{3}.
  4. Substitute values into formula: Substitute the values into the tangent subtraction formula: tan⁡(π12)=tan⁡(π4)−tan⁡(π6)1+tan⁡(π4)tan⁡(π6)=1−3/31+(1)(3/3)\tan(\frac{\pi}{12}) = \frac{\tan(\frac{\pi}{4}) - \tan(\frac{\pi}{6})}{1 + \tan(\frac{\pi}{4})\tan(\frac{\pi}{6})} = \frac{1 - \sqrt{3}/3}{1 + (1)(\sqrt{3}/3)}.
  5. Simplify the expression: Simplify the expression: tan⁡(π12)=1−3/31+3/3=3−33+3\tan\left(\frac{\pi}{12}\right) = \frac{1 - \sqrt{3}/3}{1 + \sqrt{3}/3} = \frac{3 - \sqrt{3}}{3 + \sqrt{3}}.
  6. Rationalize the denominator: Rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator: (3−33+3)⋅(3−33−3)\left(\frac{3 - \sqrt{3}}{3 + \sqrt{3}}\right) \cdot \left(\frac{3 - \sqrt{3}}{3 - \sqrt{3}}\right).
  7. Perform the multiplication: Perform the multiplication: (\(3 - \sqrt{33})^22 / (33^22 - (\sqrt{33})^22) = (99 - 66\sqrt{33} + 33) / (99 - 33) = (1212 - 66\sqrt{33}) / 66.
  8. Simplify the expression: Simplify the expression: (12−63)/6=2−3(12 - 6\sqrt{3}) / 6 = 2 - \sqrt{3}.
  9. Check the answer choices: Check the answer choices to see which one matches our result. The correct answer is (A) (3−3)/(3+3)(3 - \sqrt{3}) / (3 + \sqrt{3}), which simplifies to 2−32 - \sqrt{3} after rationalizing the denominator.

More problems from Domain and range

Question
What is the domain of this function?\newline(9,–2)(6,–10)(–3,9)(5,2)(9,–2)(6,–10)(–3,9)(5,2)\newlineChoices:\newline(A){–3,5,6,9}(B){–10,–2,2,9}(C){2,5,6,9}(D){–6,–3,5,9}(A)\{–3,5,6,9\}\newline(B)\{–10,–2,2,9\}\newline(C)\{2,5,6,9\}\newline(D)\{–6,–3,5,9\}
Get tutor helpright-arrow

Posted 1 year ago

Question
Look at this set of ordered pairs:\newline(2,14)(2, 14)\newline(10,12)(10, 12)\newline(3,−19)(3, -19)\newlineIs this relation a function?\newlineChoices:\newline[[yes]\text{[[yes]}[no]]\text{[no]]}
Get tutor helpright-arrow

Posted 1 year ago

Question
Use the following function rule to find f(11) f(11) .\newlinef(x)=−10−7x f(x) = -10 - 7x \newlinef(11)= f(11) = _____
Get tutor helpright-arrow

Posted 1 year ago

Question
Find the slope of the line y=−3x−25 y = -3x - \frac{2}{5} .\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 1 year ago

Question
A line has a slope of 33 and passes through the point (−2,−10)(-2,-10). Write its equation in slope-intercept form.\newlineWrite your answer using integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the range of this function?\newliney = |x|\newlineChoices:\newlineall real numbers\text{all real numbers}\newline{y∣y≥0}\{y \mid y \geq 0\}\newline{y∣y≤0}\{y \mid y \leq 0\}\newline{y∣y>0}\{y \mid y > 0\}
Get tutor helpright-arrow

Posted 1 year ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 1 1 unit down of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the domain of this function?\newline(8,–1)(7,–11)(–4,10)(4,3)(8,–1)(7,–11)(–4,10)(4,3)\newlineChoices: \newline(A){–4,4,7,8}(A)\{–4,4,7,8\}\newline(B){–11,–1,3,10}(B)\{–11,–1,3,10\}\newline(C){3,4,7,8}(C)\{3,4,7,8\}\newline(D){–7,–4,4,8}(D)\{–7,–4,4,8\}
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the domain of this function?\newline(10, –3)(2, –9)(–5, 8)(3, 1)(10,\,–3)(2,\,–9)(–5,\,8)(3,\,1)\newlineChoices:\newline[{–5,2,3,10}][{–9, –3,1,8}][{1,2,3,10}][{–10, –5,2,3}][\{–5,2,3,10\}][\{–9,\,–3,1,8\}][\{1,2,3,10\}][\{–10,\,–5,2,3\}]
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the domain of this function?\newline(1,–4)(9,–12)(–6,11)(7,5)(1,–4)(9,–12)(–6,11)(7,5)\newlineChoices:(A){–6,1,7,9}\newline\\(A)\{–6,1,7,9\}\newline(B){–12,–4,5,11}(B)\{–12,–4,5,11\}\newline(C{5,1,7,9}(C\{5,1,7,9\}\newline(D){–9,–6,1,7}(D)\{–9,–6,1,7\}
Get tutor helpright-arrow

Posted 1 year ago

View all (377)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant