Find an angle
$\text{\hspace{0.17em}}\alpha \text{\hspace{0.17em}}$ that is coterminal with an angle measuring 870°, where
$\mathrm{0\xb0}\le \alpha <\mathrm{360\xb0}.$
Find an angle
$\text{\hspace{0.17em}}\beta \text{\hspace{0.17em}}$ that is coterminal with an angle measuring −300° such that
$\text{\hspace{0.17em}}\mathrm{0\xb0}\le \beta <\mathrm{360\xb0}.\text{\hspace{0.17em}}$
We can find
coterminal angles measured in radians in much the same way as we have found them using degrees. In both cases, we find coterminal angles by adding or subtracting one or more full rotations.
Given an angle greater than$\text{\hspace{0.17em}}2\pi ,$find a coterminal angle between 0 and$\text{\hspace{0.17em}}2\pi .$
Subtract
$\text{\hspace{0.17em}}2\pi \text{\hspace{0.17em}}$ from the given angle.
If the result is still greater than
$\text{\hspace{0.17em}}2\pi ,$ subtract
$\text{\hspace{0.17em}}2\pi \text{\hspace{0.17em}}$ again until the result is between
$\text{\hspace{0.17em}}0\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}2\pi .\text{\hspace{0.17em}}$
The resulting angle is coterminal with the original angle.
Finding coterminal angles using radians
Find an angle
$\text{\hspace{0.17em}}\beta \text{\hspace{0.17em}}$ that is coterminal with
$\text{\hspace{0.17em}}\frac{19\pi}{4},$ where
$\text{\hspace{0.17em}}0\le \beta <2\pi .$
When working in degrees, we found coterminal angles by adding or subtracting 360 degrees, a full rotation. Likewise, in radians, we can find coterminal angles by adding or subtracting full rotations of
$\text{\hspace{0.17em}}2\pi \text{\hspace{0.17em}}$ radians:
The angle
$\text{\hspace{0.17em}}\frac{11\pi}{4}\text{\hspace{0.17em}}$ is coterminal, but not less than
$\text{\hspace{0.17em}}2\pi ,$ so we subtract another rotation:
The angle
$\text{\hspace{0.17em}}\frac{3\pi}{4}\text{\hspace{0.17em}}$ is coterminal with
$\text{\hspace{0.17em}}\frac{19\pi}{4},$ as shown in
[link] .
Find an angle of measure
$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ that is coterminal with an angle of measure
$\text{\hspace{0.17em}}-\frac{17\pi}{6}\text{\hspace{0.17em}}$ where
$\text{\hspace{0.17em}}0\le \theta <2\pi .$
Recall that the
radian measure$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ of an angle was defined as the ratio of the
arc length$\text{\hspace{0.17em}}s\text{\hspace{0.17em}}$ of a circular arc to the radius
$\text{\hspace{0.17em}}r\text{\hspace{0.17em}}$ of the circle,
$\text{\hspace{0.17em}}\theta =\frac{s}{r}.\text{\hspace{0.17em}}$ From this relationship, we can find arc length along a circle, given an angle.
Arc length on a circle
In a circle of radius
r , the length of an arc
$\text{\hspace{0.17em}}s\text{\hspace{0.17em}}$ subtended by an angle with measure
$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ in radians, shown in
[link] , is
Given a circle of radius$r,$calculate the length$s$of the arc subtended by a given angle of measure$\theta .$
If necessary, convert
$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ to radians.
Multiply the radius
$\text{\hspace{0.17em}}r\text{\hspace{0.17em}}$ by the radian measure of
$\text{\hspace{0.17em}}\theta :s=r\theta .\text{\hspace{0.17em}}$
Finding the length of an arc
Assume the orbit of Mercury around the sun is a perfect circle. Mercury is approximately 36 million miles from the sun.
In one Earth day, Mercury completes 0.0114 of its total revolution. How many miles does it travel in one day?
Use your answer from part (a) to determine the radian measure for Mercury’s movement in one Earth day.
Let’s begin by finding the circumference of Mercury’s orbit.
No because a negative times a negative is a positive. No matter what you do you can never multiply the same number by itself and end with a negative
lurverkitten
Actually you can. you get what's called an Imaginary number denoted by i which is represented on the complex plane. The reply above would be correct if we were still confined to the "real" number line.
Liam
Suppose P= {-3,1,3} Q={-3,-2-1} and R= {-2,2,3}.what is the intersection
Someone should please solve it for me
Add 2over ×+3 +y-4 over 5
simplify (×+a)with square root of two -×root 2 all over a
multiply 1over ×-y{(×-y)(×+y)} over ×y
For the first question, I got (3y-2)/15
Second one, I got Root 2
Third one, I got 1/(y to the fourth power)
I dont if it's right cause I can barely understand the question.
Is under distribute property, inverse function, algebra and addition and multiplication function; so is a combined question
graph the following linear equation using intercepts method.
2x+y=4
Ashley
how
Wargod
what?
John
ok, one moment
UriEl
how do I post your graph for you?
UriEl
it won't let me send an image?
UriEl
also for the first one... y=mx+b so.... y=3x-2
UriEl
y=mx+b
you were already given the 'm' and 'b'.
so..
y=3x-2
Tommy
Please were did you get y=mx+b from
Abena
y=mx+b is the formula of a straight line.
where m = the slope & b = where the line crosses the y-axis. In this case, being that the "m" and "b", are given, all you have to do is plug them into the formula to complete the equation.
Tommy
thanks Tommy
Nimo
0=3x-2
2=3x
x=3/2
then .
y=3/2X-2
I think
Given
co ordinates for x
x=0,(-2,0)
x=1,(1,1)
x=2,(2,4)
neil
"7"has an open circle and "10"has a filled in circle who can I have a set builder notation
I've run into this:
x = r*cos(angle1 + angle2)
Which expands to:
x = r(cos(angle1)*cos(angle2) - sin(angle1)*sin(angle2))
The r value confuses me here, because distributing it makes:
(r*cos(angle2))(cos(angle1) - (r*sin(angle2))(sin(angle1))
How does this make sense? Why does the r distribute once
this is an identity when 2 adding two angles within a cosine. it's called the cosine sum formula. there is also a different formula when cosine has an angle minus another angle it's called the sum and difference formulas and they are under any list of trig identities
Brad
strategies to form the general term
carlmark
consider r(a+b) = ra + rb. The a and b are the trig identity.
Mike
How can you tell what type of parent function a graph is ?
generally by how the graph looks and understanding what the base parent functions look like and perform on a graph
William
if you have a graphed line, you can have an idea by how the directions of the line turns, i.e. negative, positive, zero
William
y=x will obviously be a straight line with a zero slope
William
y=x^2 will have a parabolic line opening to positive infinity on both sides of the y axis
vice versa with y=-x^2 you'll have both ends of the parabolic line pointing downward heading to negative infinity on both sides of the y axis
William
y=x will be a straight line, but it will have a slope of one. Remember, if y=1 then x=1, so for every unit you rise you move over positively one unit. To get a straight line with a slope of 0, set y=1 or any integer.
Aaron
yes, correction on my end, I meant slope of 1 instead of slope of 0
Typically a function 'f' will take 'x' as input, and produce 'y' as output. As
'f(x)=y'.
According to Google,
"The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain."
Thomas
Sorry, I don't know where the "Â"s came from. They shouldn't be there. Just ignore them. :-)
Thomas
GREAT ANSWER THOUGH!!!
Darius
Thanks.
Thomas
Â
Thomas
It is the Â that should not be there. It doesn't seem to show if encloses in quotation marks.
"Â" or 'Â' ... Â