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Delvig [45]
11 months ago
14

Use the given information to find the exact value of the trigonometric function

Mathematics
1 answer:
eimsori [14]11 months ago
7 0
\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}

Half Angle Formula

\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\  \\  \end{gathered}

Answer:

\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}

Checking:

\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{  (3rd quadrant)} \end{gathered}

Also,

\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}

The answer is none of the choices

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prisoha [69]


Use two points from the graph to check if they are constant. In this case let’s use (0,50) & (2,58)

To find slope you have to do the following.

y2-y1 / x2-x1

Plug in the values, 58-50/2-0
This gives you 4.

When you use two other points, in this case (10,90) (20,130) you get a slope of 4.

This means the slope is 4.

We are trying to get an equation of y=mx+b.
We have slope already which is 4. So now we plug in y=4x + b

Now we need to find b. There is an equation to solve for b. Which is b=y1-m(x1)

But b is the y-intercept so there is already a B which is 50

So the table IS a linear equation and the equation is y=4x+50.
8 0
3 years ago
To express the polynomial d^2+d^3-d+3 in standard form, which term should be written first?
ozzi
When you want to write a polynomial, you should write the term with the highest degree first.
Here, it should go like this: d^3 + d^2 - d + 3
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6 0
3 years ago
Read 2 more answers
PLS HELP ME WITH MATH
arsen [322]

Answer:

slope is 3

Step-by-step explanation:

Slope = \frac{change  in  y }{change  in  x }

change in y = (13-7),  (19-13),  (25-19),  (31-25)

change in y = 6

Change in x = (4-2),  (6-4),  (8-6),  (10-8)

Change in x = 2

Therefore slope = \frac{6}{2}

Slope = 3

5 0
2 years ago
Dale tried to estimate the area of his backyard garden. He guessed it was 12 square meters. When he measured the dimensions late
Elena-2011 [213]

Answer:

cool

Step-by-step explanation:

5 0
2 years ago
Is 0.48 greater than 11/25
Zina [86]
0.48=48/100=12/25~~~12/25>11/25 True✔ ~~~~Have a nice day!!! ★★
8 0
3 years ago
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