Answer:

Step-by-step explanation:
First, simplify each term:

Then given expression is equivalent to
![\cos ^3\alpha+(-\sin \alpha)^3-(-\sin \alpha)+(-\cos \alpha)\\ \\=\cos ^3\alpha-\sin^3 \alpha+\sin \alpha-\cos \alpha\\ \\=(\cos\alpha-\sin\alpha)(\cos^2\alpha+\cos\alpha\sin\alpha+\sin^2\alpha)-(\cos\alpha-\sin\alpha)\\ \\=(\cos\alpha-\sin\alpha)(1+\cos\alpha\sin\alpha-1)\ \ [\cos^2\alpha+\sin^2\alpha=1]\\ \\=\cos\alpha\sin\alpha(\cos\alpha-\sin\alpha)](https://tex.z-dn.net/?f=%5Ccos%20%5E3%5Calpha%2B%28-%5Csin%20%5Calpha%29%5E3-%28-%5Csin%20%5Calpha%29%2B%28-%5Ccos%20%5Calpha%29%5C%5C%20%5C%5C%3D%5Ccos%20%5E3%5Calpha-%5Csin%5E3%20%5Calpha%2B%5Csin%20%5Calpha-%5Ccos%20%5Calpha%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%28%5Ccos%5E2%5Calpha%2B%5Ccos%5Calpha%5Csin%5Calpha%2B%5Csin%5E2%5Calpha%29-%28%5Ccos%5Calpha-%5Csin%5Calpha%29%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%281%2B%5Ccos%5Calpha%5Csin%5Calpha-1%29%5C%20%5C%20%5B%5Ccos%5E2%5Calpha%2B%5Csin%5E2%5Calpha%3D1%5D%5C%5C%20%5C%5C%3D%5Ccos%5Calpha%5Csin%5Calpha%28%5Ccos%5Calpha-%5Csin%5Calpha%29)
Answer:
Step-by-step explanation:
1) 64.04
2)16.02
9514 1404 393
Answer:
5/4
Step-by-step explanation:
The relationship between the sec and csc functions is ...
csc(A) = sec(A)/√(sec²(A) -1)
For the given value of sec(A), this is ...
csc(A) = (5/3)/√((5/3)² -1) = (5/3)/√(16/9) = (5/3)/(4/3)
csc(A) = 5/4
__
Some calculators can tell you the answer directly.
Answer
Find out the what was his total cost .
To prove
As given
A tent was marked up 150% from an original cost of $52.
Last Friday, Ethan bought the tent and paid an additional 10% in sales tax.
Than the equation becomes
150 % is written in the decimal form .

= 1.5
10 % is written in the decimal form .

= 0.1
cost of the tent when 150% marked up from origianl price = 1.5× 52
= $ 78
cost of the tent = origianl cost + 150% marked up from origianl price
= $52 + $78
= $ 130
Sales price on the tent = $130 × 0.1
= 13
Total cost of the tent = $130 + $13
= $143
Therefore the cost of the tent is $143.
Answer:
You can find the midpoint of a line segment given 2 endpoints, (x1, y1) and (x2, y2). Add each x-coordinate and divide by 2 to find x of the midpoint. Add each y-coordinate and divide by 2 to find y of the midpoint. It's important to note that a midpoint is the middle point on a line segment.
In order to see the midpoint formula in use, let's look at an example.
Question:
Determine the midpoint of the line segment with the given endpoints.
A(3, 7), B(9, 1)A(3,7),B(9,1)
Solution:
We can use the formula for midpoint to determine the midpoint: M= (x1 + x2/2 , y1+y2/2)
First, plug the x and y value into the formula:
M=(3+9/2 , 7+1/2)
,
Then, we can calculate the midpoint:
(6, 4)