Tom's backyard has an area of 25 square yards. What is its area in square inches? (1 yd = 36 in.)
1 answer:
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Answer: -4/5
Step-by-step explanation:
Ok so cos(x) = -4/5 and we know that:
.
If we plug that in and solve for sin(x) we get:
Now we have to consider: <em>is sin(x) positive or negative?</em>
We have that .
From the unit circle, we know that sin(x) is negative in this range. Therefore sin(x) actually equals -3/5.
But the question asks: <em>what is ?</em>
Here's where another important equation comes in:
In this case, we have alpha = x and beta = pi/2.
So, that looks like:
sin(x + pi/2 )= sin(x)cos(pi/2) + cos(x)sin(pi/2)
We already have what sin(x) and cos(x) are. We also know that sin( pi/2) = 1 and cos(pi/2) = 0.
sin(x + pi/2 ) = (-3/5)(0) + (-4/5)(1).
Therefore we simply have
sin(x + pi/2) = -4/5
The general slope-intercept form is given by 
, where 
is the slope and 
is the y-intercept.
Let's find the slope first. Remember that the slope given by two points is
. So, using the two given points,
Now, we know that
. To find , let's just plug in the x and y coordinates for one of the points and solve for b:
Thus, the equation of the line in slope-intercept form is
Let's find the slope first. Remember that the slope given by two points is
Now, we know that
Thus, the equation of the line in slope-intercept form is