<span>sinx - cosx =sqrt(2)
Taking square on both sides:
</span>(sinx - cosx)^2 =sqrt(2)^2<span>
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
</span><span>sin^2(x)+cos^2(x) = 1
</span><span>So,
1-2sinxcosx=2
1-1-2sinxcosx=2-1
-</span><span>2sinxcosx = 1
</span><span>Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
</span><span>sin2x = -1</span><span>
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer</span>
Answer:
5 cookies per minute.
Step-by-step explanation:
To do this, we divide 27.5 by 5.5 to get the unit rate, in other words, the amount of cookies eaten per minute. This gets us 5. That means Amy ate 5 cookies per minute.
Answer:
The area of a circular wrestling region with a 42 fr diameter is
A≈1385.44ft²
Answer:
Step-by-step explanation:
c = 50 + 0.25m
Answer:
150=6x
Step-by-step explanation:
Let x = height of the tree.
Set up the ratio %28Height%29%2F%28Shadow%29+=5%2F6=x%2F30
Since a%2Fb=c%2Fd means ad=bc,
5%2F6=x%2F30 means 5%2A30=6%2Ax
150=6x
