You can think of the points X, Y, Z as vectors originating from the origin. Each of these "vectors" would have a magnitude associated with it, found by using the Pythagorean Theorem.
For example, the magnitude of X would be sqrt(12^2 + 9^2) =...
To visualize how the graph moves, rewrite y = (x - 3)^2 + 4 so that it is easier to compare with y = x^2.
old: y = x^2
new: (y' - 4) = (x' - 3)^2
Now you can see that the transformation changed y to (y' - 4) and x to (x' - 3).
y = y' - 4 ---->...
The only numbers that square to one are 1 and -1.
1 = 1 x 1
1 = (-1) x (-1)
So since (tan x) squares to one, (tan x) must be 1 or -1. There are two values of x in the interval [0, pi] that make it happen.
tan (pi/4) = 1
tan (3*pi/4) = -1
Here is a graphical way to think of it.
Suppose you wanted to divide the number 1 by 0. In other words, you want to find y = 1/x when x = 0. Well, try graphing the function y = 1/x. You will notice that to the left of x = 0, the value of y approaches negative infinity...
One way to solve this problem is to use the Law of Sines: sin(A)/a = sin(B)/b = sin(C)/c. Here a, b, c are the lengths of the sides, and A, B, C are the angles across from (not touching) the sides a, b, c respectively.
Since you are given b, c, and B, you could...
The typical way to evaluate 67 x 436 is by multiplying and adding: (60 + 7) x 436. Usually this is written as:
3052 = 436 x 7
+ 26160 = 436 x 60
Here is a way to remember that the angles of a triangle sum to 180 degrees.
Imagine a squat triangle, with two very acute angles and one very obtuse angle. If this triangle is very stout, then the acute angles are ~0 and the obtuse angle is ~180 degrees.
Let's suppose 9 is a factor of the number N. That means N is 9 times some integer M.
N = 9*M
Since 9 = 3*3, we can also write N as
N = 3*3*M
That means N is 3 times some integer (3*M). So 3 is also a factor of N.