Answer:
the shape could be congruent or similar to its preimage. There are basically four types of transformations: Rotation; Translation; Dilation; Reflection; Definition of Transformations. Transformations could be rigid (where the shape or size of preimage is not changed) and non-rigid (where the size is changed but the shape remains the same).
Step-by-step explanation:
8-1/4n is the answer to this
Answer:
-8 and 9
Step-by-step explanation:
-8 x 9 = -72
and -8 + 9 = 1
I would compute sqrt(1 + 160pi^2) first to get approximately 39.75093337
Add this to 1 and we have 40.75093337
Then divide over 2pi to get a final approximate result of 6.48571248
So x = 6.48571248 is one approximate solution
In short, I computed 
only focusing on the plus for now.
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If you were to compute 
you should get roughly -6.167402596 as your other solution. Each solution can then be plugged into the original equation to check if you get 0 or not. You likely won't land exactly on 0 but you'll get close enough.
By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
