Answer:
An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians). It is the inverse function of the basic trigonometric functions.
Step-by-step explanation:
Trigonometric functions are derived from ratios of certain sides of a right triangle in reference to an angle. The graph of which is a wave, with amplitude in the y-axis and angle in the x-axis. We will first define the sine function written as:
sin(θ)=oppositesidehypotenuse
As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.
Let
y
=
s
i
n
(
θ
)
y=sin(θ)
Then inverse trigonometric function outputs an angle. However, we can set y to its original value via transitivity:
s
i
n
−
1
(
y
)
=
θ
s
i
n
−
1
(
o
p
p
o
s
i
t
e
s
i
d
e
h
y
p
o
t
e
n
u
s
e
)
=
θ
sin−1(y)=θsin−1(oppositesidehypotenuse)=θ
Thus we see, that the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
Answer:
Check Explanation.
Step-by-step explanation:
The sample will be a representative of the entire build us in the city.
For a sample size 35, 3 have fire code violations, hence, the proportion of houses with fire code violations = (3/35) = 0.0857 = 8.57 %
The uncertainty in the estimate is given in the form of standard error.
Standard error = √[(p(1-p)/n]
n = sample size = 35, p = 0.0857, 1 - p = 0.9143
Standard error of the sample = √(0.0857×0.9143/35) = 0.1616
In terms of the population, (0.1616/35) = 0.00462
Proportion of buildings with fire code violations = (8.57 ± 0.462) %
Answer:
Step-by-step explanation:
Do you mean an isosceles triangle? If you do then the answer is yes because two of the angles cannot be more that 90o. If they are the sum of the angles are going to be more than 180.
For example, if both angles in the isosceles triangles are 100 then the two angles will add up to 100 + 100 = 200 degrees. No triangle has 200 degrees in it.
Well how about 90.? Could two angles in a triangle have 90 each?
No because 90 + 90 = 180. There's no room for another angle.
So two angles of an isosceles triangle must be acute.
If this is not what you mean, please leave a not.