If the function y = sinx is transformed to y = 3 sine (two-thirds x), how do the amplitude and period change?
2 answers:
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You want to drwa a diagram
ok, so 10√2 yards at a 45 degree angle
alrighty
let's use a graphing plane
our starting point is at (0,0), the origin
if we go 10 right and 10 up, we end up at (10,10)
now, if we were to draw a line from our starting point (the origin) to the ending point (10,10), we get a line (duh)
if we measure the angle between the line and the x axis, we get 45 degrees
if we find the distance from (0,0) to (10,10) using the distaance formula, we get 10√2 is the distance from (0,0) to (10,10)
so going 10 out and 10 right is same as 10√2 at 45 degree angle
or you could draw a triangle (see diagram)
legs are 10 and 10, connect them to get a hypotnuse
since the legs are equal lengths, the angles are 45-45-90, we have a 45-45-90 triangle
we can either use the special properies of a 45-45-90 triangle (side lenghs are x:x:x√2) or use pythagorean
so remember if te legs are a,b,,c then a²+b²=c²
a=b=10
10²+10²=c²
100+100=c²
200=c²
sqrt both sides
10√2=c
the lenght is 10√2 at a 45 degree angle
ok, so 10√2 yards at a 45 degree angle
alrighty
let's use a graphing plane
our starting point is at (0,0), the origin
if we go 10 right and 10 up, we end up at (10,10)
now, if we were to draw a line from our starting point (the origin) to the ending point (10,10), we get a line (duh)
if we measure the angle between the line and the x axis, we get 45 degrees
if we find the distance from (0,0) to (10,10) using the distaance formula, we get 10√2 is the distance from (0,0) to (10,10)
so going 10 out and 10 right is same as 10√2 at 45 degree angle
or you could draw a triangle (see diagram)
legs are 10 and 10, connect them to get a hypotnuse
since the legs are equal lengths, the angles are 45-45-90, we have a 45-45-90 triangle
we can either use the special properies of a 45-45-90 triangle (side lenghs are x:x:x√2) or use pythagorean
so remember if te legs are a,b,,c then a²+b²=c²
a=b=10
10²+10²=c²
100+100=c²
200=c²
sqrt both sides
10√2=c
the lenght is 10√2 at a 45 degree angle