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:

Use the reference angle to find the exact value of the given expression.\newlinecos⁡(7π6)\cos \left(\frac{7\pi}{6}\right)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Roots of rational numbersright chevron icon

Full solution

Q. Use the reference angle to find the exact value of the given expression.\newlinecos⁡(7π6)\cos \left(\frac{7\pi}{6}\right)
  1. Identify Reference Angle: Identify the reference angle for (7π)/6(7\pi)/6. Since (7π)/6(7\pi)/6 is in the third quadrant (more than π\pi but less than 3π/23\pi/2), the reference angle is π−(7π)/6=(6π)/6−(7π)/6=−(π)/6\pi - (7\pi)/6 = (6\pi)/6 - (7\pi)/6 = -(\pi)/6.
  2. Determine Cosine: Determine the cosine of the reference angle.\newlineThe cosine of (π)/6(\pi)/6 is 3/2\sqrt{3}/2. Since the cosine is positive in the first quadrant and we are looking for the cosine of the negative of this angle, it remains positive: cos⁡(−(π)/6)=cos⁡((π)/6)=3/2\cos(-(\pi)/6) = \cos((\pi)/6) = \sqrt{3}/2.
  3. Apply Function Behavior: Apply the cosine function's behavior in different quadrants.\newlineIn the third quadrant, where (7π)/6(7\pi)/6 lies, the cosine function is negative. Therefore, we must take the negative of the reference angle's cosine value.
  4. Combine Results: Combine the results to find the exact value.\newlineThe exact value of cos⁡(7π6)\cos\left(\frac{7\pi}{6}\right) is −3/2-\sqrt{3}/2.

More problems from Roots of rational numbers

Question
Find the real-number root. \newline16\sqrt{16}\newline\newlineWrite your answer in simplified form. \newline____\_\_\_\_
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the real-number root. \newline916\sqrt{\frac{9}{16}}\newlineSimplify your answer and write it as a decimal or as a proper or improper fraction.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the real-number root using a calculator. Round your answer to the nearest thousandth. \newline`\sqrt{957} `\newline _______
Get tutor helpright-arrow

Posted 9 months ago

Question
Multiply. Write your answer in simplest form. \newline273×42\sqrt{273} \times \sqrt{42}\newline______
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify. \newline634\sqrt{\frac{63}{4}}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Rationalize the denominator.\newline−49−2\frac{-4}{9 - \sqrt{2}}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for z z .\newline16=z 16 = \sqrt{z} \newlinez= z = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify the radical expression. 14x14 \sqrt{14x^{14}} Write your answer in the form A A , B \sqrt{B} , or AB A\sqrt{B} , where A A and B B are constants or expressions in x x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A A . ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify the radical expression.\newline12x12\sqrt{12x^{12}}\newlineWrite your answer in the form AA, B\sqrt{B}, or ABA\sqrt{B}, where AA and BB are constants or expressions in xx. Use at most one radical in your answer, and at most one absolute value symbol in your expression for AA.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the value of sin⁡(5π6)? \sin \left(\frac{5 \pi}{6}\right) ? \newlineChoose 11 answer:\newline(A) −32 -\frac{\sqrt{3}}{2} \newline(B) −22 -\frac{\sqrt{2}}{2} \newline(C) 12 \frac{1}{2} \newline(D) 150150
Get tutor helpright-arrow

Posted 10 months ago

View all (169)

Related topics

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