Give the exact value of the trigonometric function.
csc225°
A. [tex]\sqrt{2}[/tex]
B. [tex]\frac{\sqrt{2} }{2}[/tex]
C. [tex]-\sqrt{2}[/tex]
D. [tex]\frac{-\sqrt{2} }{2}[/tex]
Please explain your answer, I will give brainliest, thank you!
Answers
Answer:
[tex] \displaystyle \text C)\csc( {225}^{ \circ } )= - \sqrt{2} [/tex]
Step-by-step explanation:
we want to figure out the exact value of the following:
[tex] \displaystyle \csc( {225}^{ \circ} ) [/tex]
recall that,
[tex] \displaystyle \csc( \theta ) = \frac{1}{ \sin( \theta)} [/tex]
we are given [tex]\theta=225°[/tex]
substitute:
[tex] \displaystyle \csc( {225}^{ \circ } )= \frac{1}{ \sin( {225}^{ \circ} )} [/tex]
225° belongs to Q:III which we can clearly acquire from unit circle so,
[tex] \displaystyle \csc( {225}^{ \circ } )= \frac{1}{ \dfrac{ - \sqrt{2} }{2} } [/tex]
By simplifying complex fraction we get:
[tex] \displaystyle \csc( {225}^{ \circ } )= \frac{2}{ - \sqrt{ 2} } [/tex]
notice that, what we acquired isn't in the option so multiply it by √2/√2
[tex] \displaystyle \csc( {225}^{ \circ } )= \frac{2}{ - \sqrt{ 2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } [/tex]
simplify multiplication:
[tex] \displaystyle \csc( {225}^{ \circ } )= \frac{2 \sqrt{2} }{ - \sqrt{ 4} } [/tex]
simplify square:
[tex] \displaystyle \csc( {225}^{ \circ } )= \frac{2 \sqrt{2} }{ - 2} [/tex]
reduce fraction:
[tex] \displaystyle \csc( {225}^{ \circ } )= - \sqrt{2} [/tex]
hence,
our answer is C
![Give The Exact Value Of The Trigonometric Function.csc225A. [tex]\sqrt{2}[/tex]B. [tex]\frac{\sqrt{2}](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/7TLJtSoakQbsBhoEB1Nr4pr5003upE5f.jpeg)
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*40 people responded that they use mouthwash.
*Of the people who use mouthwash, 30 people use floss.
*55 people responded that they do not floss.
*45 people responded that they don't floss and don't use mouthwash
Answers
Answer: The image of the completed table is shown below
In the completed table, we have the following values (left to right)
Row One: 30, 10, 40Row Two: 15, 45, 60Row Three: 45, 55, 100==============================================
Explanation:
We're told that "40 people responded that they use mouthwash". That means we'll write "40" at the very end of the "use mouthwash" row. This represents the total number of people who use mouthwash, since we're underneath the "total" in that far right column.
Then we're further told that "Of the people who use mouthwash, 30 people use floss", so we'll write "30" in the first row, first column blank space. These are the people who both floss and use mouthwash. Because earlier we know 40 people use mouthwash overall, this leaves 40-30 = 10 people who use mouthwash, but they don't floss.
To summarize so far: In row 1, we have the following values from left to right: 30, 10, 40
The first two items of this row must add to the last item.
---------------------
Now onto row 2
Since 40 people use mouthwash, and 100 people were surveyed, this means that 100-40 = 60 people do not use mouthwash. The value 60 goes at the very end of row 2. This represents another total.
Like earlier, the first two items must add to the last. So 40+60 = 100.
Now turn to the fact that "45 people responded that they don't floss and don't use mouthwash". This tells us that "45" will be in the "no mouthwash" row and "don't floss" column.
We have 60 people who don't use mouthwash, and 45 of those people also don't floss. Therefore, 60-45 = 15 people do floss but they don't use mouthwash. We'll write "15" in the second row, first column.
Along row 2, we have the following values: 15, 45, 60
----------------------
Row 3
For each column, add up the first two items to get the third one. This will lead to the totals along this bottom row.
Floss: 30+15 = 45Don't Floss: 10+45 = 55 .... note how this matches up with the third piece of information your teacher providedThe third column is already done, but again we can see that 40+60 = 100.
Furthermore, the first two items of the third row add to 45+55 = 100 which helps confirm our answers.
The full completed table is shown below.
------------------------
To summarize, we are effectively just sorting the values given to us to write them into the table. Then we use a bit of algebraic detective work to find out what values are missing so we fill out the completed table.