Report in math
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This document contains information about the graphs of three trigonometric functions: sine, cosine, and tangent. It describes their domains, ranges, periods, intercepts, points of maxima and minima, symmetries, and intervals of increase and decrease. The sine and cosine functions have a domain and range of all real numbers and a period of 2π. They are both odd/even functions with x-intercepts at integer multiples of π. The tangent function has a domain of all real numbers except integer multiples of π/2, with a range and period of all real numbers and π, respectively. It is an odd function with vertical asymptotes at integer multiples of π/2.
![ Domain: all real numbers
Range: [-1 , 1]
Period = 2pi
x intercepts: x = k pi , where k is an integer.
y intercepts: y = 0
maximum points: (pi/2 + 2 k pi , 1) , where k is an integer.
minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer.
symmetry: since sin(-x) = - sin (x) then sin (x) is an odd
function and its graph is symmetric with respect to the
origon (0 , 0).
intervals of increase/decrease: over one period and from 0
to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2
, 2pi), and decreasing on the interval (pi/2 , 3pi/2).](https://image.slidesharecdn.com/reportinmath-121022061857-phpapp02/85/Report-in-math-4-320.jpg)
![ Domain: all real numbers
Range: [-1 , 1]
Period = 2pi
x intercepts: x = pi/2 + k pi , where k is an integer.
y intercepts: y = 1
maximum points: (2 k pi , 1) , where k is an integer.
minimum points: (pi + 2 k pi , -1) , where k is an integer.
symmetry: since cos(-x) = cos (x) then cos (x) is an even
function and its graph is symmetric with respect to the y
axis.
intervals of increase/decrease: over one period and from
0 to 2pi, cos (x) is decreasing on (0 , pi) increasing on (pi ,
2pi).](https://image.slidesharecdn.com/reportinmath-121022061857-phpapp02/85/Report-in-math-6-320.jpg)
Report in math
- 4. Domain: all real numbers Range: [-1 , 1] Period = 2pi x intercepts: x = k pi , where k is an integer. y intercepts: y = 0 maximum points: (pi/2 + 2 k pi , 1) , where k is an integer. minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer. symmetry: since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origon (0 , 0). intervals of increase/decrease: over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2).
- 6. Domain: all real numbers Range: [-1 , 1] Period = 2pi x intercepts: x = pi/2 + k pi , where k is an integer. y intercepts: y = 1 maximum points: (2 k pi , 1) , where k is an integer. minimum points: (pi + 2 k pi , -1) , where k is an integer. symmetry: since cos(-x) = cos (x) then cos (x) is an even function and its graph is symmetric with respect to the y axis. intervals of increase/decrease: over one period and from 0 to 2pi, cos (x) is decreasing on (0 , pi) increasing on (pi , 2pi).
- 7. Domain: all real numbers except pi/2 + k pi, k is an integer. Range: all real numbers Period = pi x intercepts: x = k pi , where k is an integer. y intercepts: y = 0 symmetry: since tan(-x) = - tan(x) then tan (x) is an odd function and its graph is symmetric with respect the origin. intervals of increase/decrease: over one period and from -pi/2 to pi/2, tan (x) is increasing. Vertical asymptotes: x = pi/2 + k pi, where k is an integer.