Use the given graph to determine the limit, if it exists. (4 points) A coordinate graph is shown with an upward sloped line cros
sing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3. Find limit as x approaches three from the right of f of x.
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Hi there!
To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).
<u>F</u><u>i</u><u>r</u><u>s</u><u>t</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>
What we have to do is to isolate cos first.
Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.
Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>2</u>
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>3</u>
<u></u>
Both values are apart of the interval. Hence,
<u>S</u><u>e</u><u>c</u><u>o</u><u>n</u><u>d</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>
Isolate sin(4 theta).
Rationalize the denominator.
The problem here is 4 beside theta. What we are going to do is to expand the interval.
Multiply whole by 4.
Then find the reference angle.
We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.
sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>3</u>
<u></u>
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>4</u>
Both values are in [0,2π). However, we exceed our interval to < 8π.
We will be using these following:-
Hence:-
<u>F</u><u>o</u><u>r</u><u> </u><u>Q</u><u>3</u>
We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.
<u>F</u><u>o</u><u>r</u><u> </u><u>Q</u><u>4</u>
Therefore:-
Then we divide all these values by 4.
Let me know if you have any questions!
