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:

In the diagram below, the circle has a radius length of r=4 r = 4 . If the measure of central angle AB=115 AB = 115 °, then what is the area of the unshaded part of the circle O O ?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Complementary angle identitiesright chevron icon

Full solution

Q. In the diagram below, the circle has a radius length of r=4 r = 4 . If the measure of central angle AB=115 AB = 115 °, then what is the area of the unshaded part of the circle O O ?
  1. Calculate Circle Area: Calculate the area of the entire circle.\newlineThe formula for the area of a circle is A=πr2A = \pi r^2, where rr is the radius of the circle.\newlineGiven r=4r = 4, we calculate the area as follows:\newlineA=π(4)2=16πA = \pi(4)^2 = 16\pi square units.
  2. Calculate Shaded Fraction: Calculate the fraction of the circle that is shaded by the central angle.\newlineThe central angle of the shaded sector is 115∘115^\circ. The fraction of the circle that this sector represents is given by the central angle over 360∘360^\circ.\newlineFraction of circle = Central angle / 360∘360^\circ = 115∘/360∘115^\circ / 360^\circ.
  3. Calculate Shaded Sector Area: Calculate the area of the shaded sector.\newlineUsing the fraction from Step 22, we multiply it by the total area of the circle to find the area of the shaded sector.\newlineArea of shaded sector = Fraction of circle ×\times Area of entire circle = (115°/360°)×16π(115° / 360°) \times 16\pi.\newlineArea of shaded sector = (115/360)×16π≈10.2222π(115 / 360) \times 16\pi \approx 10.2222\pi square units.
  4. Calculate Unshaded Area: Calculate the area of the unshaded part of the circle.\newlineTo find the area of the unshaded part, we subtract the area of the shaded sector from the total area of the circle.\newlineArea of unshaded part = Area of entire circle - Area of shaded sector = 16π−10.2222π16\pi - 10.2222\pi.\newlineArea of unshaded part ≈5.7778π\approx 5.7778\pi square units.

More problems from Complementary angle identities

Question
If cos⁡(θ)=817 \cos(\theta)=\frac{8}{17} and 0∘<θ<90∘ 0^\circ<\theta<90^\circ , what is sec⁡(θ) \sec(\theta) ? Write your answer in simplified, rationalized form. sec⁡(θ)= \sec(\theta)= ______
Get tutor helpright-arrow

Posted 2 months ago

Question
cos⁡(x)=−0.3\cos(x) = -0.3. What is sin⁡(90∘−x)\sin(90^\circ - x)? ____
Get tutor helpright-arrow

Posted 2 months ago

Question
If csc⁡(θ)=178 \csc(\theta) = \frac{17}{8} and 0∘<θ<90∘ 0^\circ < \theta < 90^\circ , what is tan⁡(θ) \tan(\theta) ?\newlineWrite your answer in simplified, rationalized form.\newlinetan⁡(θ)= \tan(\theta) = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Is the sine function even or odd?\newlineChoices:\newline[A]even\text{[A]even}\newline[B]odd\text{[B]odd}
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the sentence as an equation. \newline8989 is equal to the quotient of yy and 1717 \newlineType a slash ( / / ) if you want to use a division sign. \newline_____
Get tutor helpright-arrow

Posted 1 month ago

Question
Write the sentence as an equation. \newline4545 is equal to the quotient of zz and 55 \newlineType a slash ( / / ) if you want to use a division sign. \newline_____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for hh. \newline h2+24h=0h^2 + 24h = 0 \newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newline h=h = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
h2−4h=0h^2 - 4h = 0
Get tutor helpright-arrow

Posted 1 month ago

Question
Combine the like terms to create an equivalent expression:\newline−k−(−8k)=□-k-(-8k)=\square
Get tutor helpright-arrow

Posted 4 months ago

Question
Which of the following degree measures is equal to 5π 5 \pi radians?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) 144∘ 144^{\circ} \newline(B) 900∘ 900^{\circ} \newline(C) 1,080∘ 1,080^{\circ} \newline(D) 1,800∘ 1,800^{\circ}
Get tutor helpright-arrow

Posted 1 month ago

View all (35)