Hey guys, I\'m having some difficulties with some of my calculus work. Question

Question

Hey guys, I'm having some difficulties with some of my calculus work.

Question 1: Find the area of a sector if the central angle measures 135 degrees and the radius of the circle is 6 inches.

Question 2: Write the equation for a sine function with an amplitude of 4 and a period of 4?/3.

Question 3: Write and equation of the cosine function with amplitude 3, period ?, phase shift -3?/4, and vertical shift -3. Thank you for any and all help! I've been sick the past 2 weeks and been going to doctor's appointments and in and out of the hospital, so I haven't been able to go to my lessons, trying to catch up!

Explanation / Answer

1. Area of a circle is pi*r^2
A sector of 135 degrees is 135/360 of a circle.

2. General sine function (no phase shift): y = A sin(w t). The amplitude is A. The period is 2pi/w.

3. General cosine function with phase shift and vertical shift: y = A cos(wt + phi) + y0
The phase shift is -phi, the vertical shift is y0. A and w are as in #2.

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