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Delvig [45]
1 year ago
14

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

Mathematics
1 answer:
eimsori [14]1 year 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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Answer:

∠ 1 = 120°

Step-by-step explanation:

Note that ∠ Q and ∠ R are congruent, that is both 30°, thus

∠ 1 = 180° - (30 + 30)° = 180° - 60° = 120°

6 0
3 years ago
Angle e measures 126LaTeX: ^\circ∘. What is the measure of LaTeX: \angle∠h?
SVEN [57.7K]

Answer:

m\angle h=126^o      

Step-by-step explanation:

we know hat

<u><em>Vertical Angles</em></u> are the angles opposite each other when two lines cross. They are always congruent.

In this problem

m\angle h=m\angle e ----> by vertical angles

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m\angle e=126^o ---> given problem

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3 0
3 years ago
Which inequality best represents that ice cream at −2°C is cooler than ice cream at 3°C? Group of answer choices −3°C &gt; 2°C −
ollegr [7]

Answer:

3°C > - 2°C

Step-by-step explanation:

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Ice cream 2 = 3°C

Lower temperatures are colder (cooler) than higher temperature values.

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Hence, a temperature of 3°C is higher (greater) than - 2°C. Hence - 2°C is cooler (colder) than 3°C

Hence,

3°C > - 2°C

5 0
2 years ago
What is the answer? ​
mr Goodwill [35]

Answer:

(write this in the format your curriculum suggests, most are different)

Since BC is longer than AB, this means m<bcd is smaller than m<bad.

A way to prove it mathematically is to look at the triangle on the left. Since It's an isosceles triangle, m<cda and m<dac are equal. However, the triangle on the right does not have two proven congruent sides. All we know is BC is larger than the other side lengths. In a figure like that, the obtuse angle that meets the longest side would be the largest angle.

Apologies for being so wordy.

4 0
3 years ago
Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes eight hours. They wor
borishaifa [10]

Answer:

10 hours to do it

Step-by-step explanation:

8-6= 2

8+2=10

5 0
3 years ago
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