the pattern blocks in a box are quadrilateral except for one. What shape could the block be that is not a quadrilateral be
1 answer:
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Let
(that is the range of the inverse sine function).
So,
![\mathsf{sin\,\theta=sin\!\left[sin^{-1}(x)\right]}\\\\ \mathsf{sin\,\theta=x\qquad\quad(i)}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3Dsin%5C%21%5Cleft%5Bsin%5E%7B-1%7D%28x%29%5Cright%5D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bsin%5C%2C%5Ctheta%3Dx%5Cqquad%5Cquad%28i%29%7D)
Square both sides:
Since
then 
is positive. So take the positive square root and you get
Then,
![\mathsf{tan\,\theta=\dfrac{sin\,\theta}{cos\,\theta}}\\\\\\ \mathsf{tan\,\theta=\dfrac{x}{\sqrt{1-x^2}}}\\\\\\\\ \therefore~~\mathsf{tan\!\left[sin^{-1}(x)\right]=\dfrac{x}{\sqrt{1-x^2}}\qquad\qquad -1\ \textless \ x\ \textless \ 1.}](https://tex.z-dn.net/?f=%5Cmathsf%7Btan%5C%2C%5Ctheta%3D%5Cdfrac%7Bsin%5C%2C%5Ctheta%7D%7Bcos%5C%2C%5Ctheta%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Btan%5C%2C%5Ctheta%3D%5Cdfrac%7Bx%7D%7B%5Csqrt%7B1-x%5E2%7D%7D%7D%5C%5C%5C%5C%5C%5C%5C%5C%20%5Ctherefore~~%5Cmathsf%7Btan%5C%21%5Cleft%5Bsin%5E%7B-1%7D%28x%29%5Cright%5D%3D%5Cdfrac%7Bx%7D%7B%5Csqrt%7B1-x%5E2%7D%7D%5Cqquad%5Cqquad%20-1%5C%20%5Ctextless%20%5C%20x%5C%20%5Ctextless%20%5C%201.%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function sin tan arcsin trigonometry</em>
_______________
Let
(that is the range of the inverse sine function).
So,
Square both sides:
Since
Then,
I hope this helps. =)
Tags: <em>inverse trigonometric function sin tan arcsin trigonometry</em>
Answer:
Option D is correct.
Explanation:
Commutative Property of Multiplication define that two numbers can be multiplied in any order.
i.e
Distributive property of multiplication states that when a number is multiplied by the sum of two numbers i.e, the first number can be distributed to both of those numbers and multiplied by each of them separately.
Associative property of multiplication states that multiplication allows us to group factors in different ways to get the same product.
Given:
A =
B =
C =
then;
Using Commutative property of Multiplication we can write then we have;
Using Distributive property of multiplication;
by using associative property of multiplication ,
Therefore, the reasons for A , B and C in this proof are;
A.commutative property of multiplication
B. distributive property
C. associative property of multiplication
Answer:
Sorry if my hand writing is bad. I didnt have a calculator for c so idk what it is
