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
FromTheMoon [43]
2 years ago
8

If θ is an angle in standard position that terminates in Quadrant III such that cosθ = -3/5, then tan =θ/2 _____.

Mathematics
1 answer:
Step2247 [10]2 years ago
7 0

Answer:

\tan\frac{\theta}{2}=-2

Step-by-step explanation:

Since\ \theta\ in\ Quadrant\ III\\\Let\ \theta=180+\phi\\\\\cos\theta=-\frac{3}{5}\\\\\cos(180+\phi)=-\frac{3}{5}\\\\-\cos\phi=-\frac{3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ as\ \cos(180+x)=-\cos x\\\\\cos\phi=\frac{3}{5}\\\\2\cos^2\frac{\phi}{2}-1=\frac{3}{5}\ \ \ \ \ \ \ \ \ \ as\ \cos x=2\cos^2\frac{x}{2}-1\\\\2\cos^2\frac{\phi}{2}=1+\frac{3}{5}=\frac{8}{5}\\\\\cos^2\frac{\phi}{2}=\frac{8}{5\times 2}\\\\\cos^2\frac{\phi}{2}=\frac{4}{5}

\cos\frac{\phi}{2}=\sqrt{\frac{4}{5}}\ \ \ \ \ positive\ sign\ is\ taken\ as\ \frac{\phi}{2}\ is\ in\ first\ quadrant\ and\ \cos\ is\ positive\ there.\\\\\sin\frac{\phi}{2}=\sqrt{1-\cos^2\frac{\phi}{2}}=\sqrt{1-\frac{4}{5}}=\sqrt\frac{1}{5}\\\\\theta=180+\phi\\\\divide\ by\ 2\\\\\frac{\theta}{2}=\frac{180+\phi}{2}\\\\\frac{\theta}{2}=90+\frac{\phi}{2}\\\\\tan\frac{\theta}{2}=\tan(90+\frac{\phi}{2})\\\\\tan\frac{\theta}{2}=-\cot\frac{\phi}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ as\ \tan(90+x)=-\cot x\tan\frac{\theta}{2}=-\frac{\cos\frac{\phi}{2}}{\sin\frac{\phi}{2}}\\\\\tan\frac{\theta}{2}=-\frac{\sqrt{\frac{4}{5}}}{\sqrt{\frac{1}{5}}}\\\\\tan\frac{\theta}{2}=-\sqrt{\frac{4}{1}}\\\\\tan\frac{\theta}{2}=-2

You might be interested in
Approximately how many degrees does five radians equal
grin007 [14]

1 radian = 180/pi
5 radians = x

X= 5• 180/pi
= 900/pi
= 286.6
6 0
3 years ago
A triangle with side lengths of 12in 16in and 24 inches is a right triangle<br>true or false​
satela [25.4K]

Answer:

False.

Step-by-step explanation:

The legs of a right triangle must have equal lengths and none of these are the same length.

6 0
3 years ago
Insert parentheses in expression 2 so that it has a value of 4. Then show why your expression has a value of 4.
Natasha_Volkova [10]
(2^3 +4) = 12

9-6=3

(2^3 +4) /(9-6)
12 /3
4
8 0
3 years ago
Will up-vote!
klasskru [66]
19.2 * 10⁸ minutes.

60 minutes = 1 hour.

19.2 * 10⁸ minutes =  (19.2 * 10⁸) / 60  hour
                 
                              = 32 000 000 =   3.2 * 10⁷ hours

= <span>D. 3.200 × 10^7 ​h​</span>
3 0
3 years ago
Assume that y varies directly with x. If y=9 when x=−3, find x when y=6.
Dafna1 [17]

Answer:-2

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Robert was able to travel 292 miles in 4 hours and uses 38 l of gasoline. if gas costs $2.09 per gallon, how much did the trip c
    7·2 answers
  • Convert: 8.9 mm = cm
    9·2 answers
  • Josie is making pizza dough. Complete the double number line by filling in the missing values. Then write an equation that model
    15·1 answer
  • Find the following f(g(x)) when<br><br> f(x)=2x+4 and g(x)=2x
    5·2 answers
  • What is the length of the line?
    14·2 answers
  • In a game you are required to pull a letter from a bag that contains one of each vowel in the alphabet (A, E, I, O, and U) and t
    9·2 answers
  • How do u simplify I dont understand it or know how to do it
    9·1 answer
  • The temperature at a mountain base camp was −2 degrees Celsius on Thursday. Friday morning, the temperature was 1 degree Celsius
    11·2 answers
  • 6 – 2x = 24<br> -6<br> - 6<br> 2x = 18<br> 2 2<br> x = 9<br> Is this statement true or false?
    13·1 answer
  • Saul makes trail mix with peanuts, raisins, and pretzels. The ratio of cups of raisins to cup of peanut is 1 to 6. The ratio of
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!