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lisabon 2012 [21]
3 years ago
11

Find sin q if q is an angle in standard position and the point with coordinates (4, 3) lies on the terminal side of the angle.

Mathematics
2 answers:
White raven [17]3 years ago
8 0
Terminal side of the position is (5,3)
zloy xaker [14]3 years ago
7 0
First we imagine triangle. Triangle vertices are: xy coordinate center, point (4,3) and projection of that point on x axis (x = 4). Because angle is in standard position, just from knowing (4,3) coordinates we know 2 of triangle sides and we can find its hypotenuse which will be marked as "h":

h= \sqrt{ 3^{2} + 4^{2} } =5

Now the sinq is:

sinq = 3/5   because of definition of sin.

sin = opposite side of triangle/hypotenuse.

answer is 3/5
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2 years ago
A, b, c and d are positive integers, such that a+b+ ab = 76, c+d+ cd = 54. Find (a+b+c+d)·a·b·c·d.
lutik1710 [3]

Notice that

(1 + <em>x</em>)(1 + <em>y</em>) = 1 + <em>x</em> + <em>y</em> + <em>x y</em>

So we can add 1 to both sides of both equations, and we use the property above to get

<em>a</em> + <em>b</em> + <em>a b</em> = 76  ==>  (1 + <em>a</em>)(1 + <em>b</em>) = 77

and

<em>c</em> + <em>d</em> + <em>c d</em> = 54  ==>  (1 + <em>c</em>)(1 + <em>d</em>) = 55

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<em>b</em> + 1 = 11  ==>  <em>b</em> = 10

(or the other way around, since the given relations are symmetric)

and

<em>c</em> + 1 = 5  ==>  <em>c</em> = 4

<em>d</em> + 1 = 11  ==>  <em>d</em> = 10

Now substitute these values into the desired quantity:

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