4. Given a circle of radius 6 with the sector shaded as shown in the figure. (a) Find the angle \( \theta \) subtended at the center when arc length is \( s = 2\pi \). (b) Find the area of the sector formed by the arc \( s \). (c) Find the area of the triangle formed by the two radii \( r \). (d) Find the area of the shaded region. *** The figure shows a circle with radius \( r = 6 \). A sector is highlighted, with the angle \( \theta \) at the center and the arc length marked as \( s = 2\pi \). The two radii forming the sector meet the circle at the arc's endpoints. The shaded region is the area of interest. 3. Given \( f(x) = 4 \sin(2x - \frac{\pi}{2}) + 1 \) (a) Put it in standard form \( y = a \cos[k(x - b)] + v \). (b) Find the amplitude, period and crunch factor, the horizontal, and vertical shift. (c) Find the interval for one cycle, build a table of values and graph the function.
4. Given a circle of radius 6 with the sector shaded as shown in the figure. (a) Find the angle \( \theta \) subtended at the center when arc length is \( s = 2\pi \). (b) Find the area of the sector formed by the arc \( s \). (c) Find the area of the triangle formed by the two radii \( r \). (d) Find the area of the shaded region. *** The figure shows a circle with radius \( r = 6 \). A sector is highlighted, with the angle \( \theta \) at the center and the arc length marked as \( s = 2\pi \). The two radii forming the sector meet the circle at the arc's endpoints. The shaded region is the area of interest. 3. Given \( f(x) = 4 \sin(2x - \frac{\pi}{2}) + 1 \) (a) Put it in standard form \( y = a \cos[k(x - b)] + v \). (b) Find the amplitude, period and crunch factor, the horizontal, and vertical shift. (c) Find the interval for one cycle, build a table of values and graph the function.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
please show work , thank you
Transcribed Image Text:4. Given a circle of radius 6 with the sector shaded as shown in the figure.
(a) Find the angle \( \theta \) subtended at the center when arc length is \( s = 2\pi \).
(b) Find the area of the sector formed by the arc \( s \).
(c) Find the area of the triangle formed by the two radii \( r \).
(d) Find the area of the shaded region.
***
The figure shows a circle with radius \( r = 6 \). A sector is highlighted, with the angle \( \theta \) at the center and the arc length marked as \( s = 2\pi \). The two radii forming the sector meet the circle at the arc's endpoints. The shaded region is the area of interest.
![3. Given \( f(x) = 4 \sin(2x - \frac{\pi}{2}) + 1 \)
(a) Put it in standard form \( y = a \cos[k(x - b)] + v \).
(b) Find the amplitude, period and crunch factor, the horizontal, and vertical shift.
(c) Find the interval for one cycle, build a table of values and graph the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21b4e0fd-2deb-4010-bcaa-5e17a99ed39c%2F2dfe79f5-57a7-449b-875a-6fe3a36cc5ae%2Fv4iy7t_processed.png&w=3840&q=75)
Transcribed Image Text:3. Given \( f(x) = 4 \sin(2x - \frac{\pi}{2}) + 1 \)
(a) Put it in standard form \( y = a \cos[k(x - b)] + v \).
(b) Find the amplitude, period and crunch factor, the horizontal, and vertical shift.
(c) Find the interval for one cycle, build a table of values and graph the function.
Expert Solution
Step 1
4).
As we know that the expression for the arc length of the circle is:
Where is the radius of the circle, is the angle subtended at the center.
(a).
Given:
Now recall the above expression and substitute these values.
Therefore,
The angle subtended at the center:
Step by step
Solved in 2 steps with 1 images
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