1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Solve x TN = 8 nV =x - 2?
AleksandrR [38]

Answer:

10

Step-by-step explanation:

STUV is a parallelogram.

TV and SU are its diagonals intersecting at point N.

Diagonals of a parallelogram bisects each other.

Therefore, TN = NV

8 = x - 2

8 + 2 = x

10 = x

x = 10

7 0
3 years ago
Find the length of an arc with central angle of 40° and radius 1
VLD [36.1K]
The arc length is 0.69813170079773
8 0
3 years ago
What is the solution to the inequality? 4x−5>19−8x
Nostrana [21]

Answer:

x>1.16

Step-by-step explanation:

Subtract 5 from each side to get 4x>14-8x

change the symbol from +8 to -8

4x> 14+ (-8x)

than add 8x to both sides

12x > 14

which would mean that x has to be greater than 1.16

x>1.16

7 0
3 years ago
(4-9-8)÷3×3please help AFAP​
Elenna [48]

Answer:

I am not really sure but try this -13/9 or -13 divided by 9

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Sarah is going to the store to buy bread for a picnic. She needs twice as many slices of bread than cheese slices. She has 24 ch
Anastaziya [24]

Answer:

4 bags of bread

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Choose the correct simplification of the expression a to the 7th power times b to the 8th power all over a to the 4th power time
    6·2 answers
  • If A = (0,0) and B = (2,5), what is the approximate length of AB?
    9·2 answers
  • The probability of spinning a 7 on a spinner is 0.083. If you spun 250 times, approximately how many times would the spinner lan
    13·2 answers
  • What is the answer to 90x144?
    9·1 answer
  • Help!!!!!!!!!!!!!!!!!!
    15·1 answer
  • GUYS PLS HELP ME<br><br> ITZ MY LAST ASSIGNMENT I NEED AND I DONT KNOW HOW TO DO ITTTT
    5·2 answers
  • Solve:
    7·1 answer
  • Un automovilista conduce hacia el norte durante 35.0 minutos a 23.61 m/s y ¿Cuál es su desplazamiento?
    9·1 answer
  • How many solutions can be found in this equation 4x - 8 - 4x = 9?
    8·1 answer
  • I need to find the value of x given the answer in simplest radical form
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!