Answer:
Using trigonometric ratio:
From the given statement:
and sin < 0
⇒ lies in the 3rd quadrant.
then;
Using trigonometry identities:
Substitute the given values we have;
Since, sin < 0
⇒
now, find :
Substitute the given values we have;
Therefore, the exact value of:
(a)
(b)
Step-by-step explanation:
Step 1:
(3x + 12y) + (10x - 5y)
<em>{Distributive property A(B+C)=AB+AC}</em>
-------------------
Step 2:
(3x + 12y) + (-5y + 10x)
<em>{Commutative property A+B = B+A}</em>
-------------------
Step 3:
3x + (12y - 5y) + 10x
<em>{Associative property A+(B+C)=(A+B)+C}</em>
-------------------
Step 4:
3x + 10x + (12y - 5y)
<em>{Commutative property A+B = B+A}</em>
-------------------
Step 5:
13x + 7y
<em>{Simplification}</em>
-------------------
No. Translation of a figure means just sliding it elsewhere. Thus, the orientation of the figure cannot be changed after the translation. There are other transformations of the figure that can change its orientation, such as reflection or rotation.