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
Dominik [7]
3 years ago
11

If sin theta= - 5/7, which of the following are possible?

Mathematics
1 answer:
Sphinxa [80]3 years ago
6 0

Answer:

\large\boxed{\sec\theta=\dfrac{7}{\sqrt{24}},\ and\ \tan\theta=-\dfrac{5}{\sqrt{24}}}\\\boxed{\cos\theta=\dfrac{\sqrt{24}}{7},\ and\ \tan\theta=\dfrac{5}{\sqrt{24}}}

Step-by-step explanation:

\text{Use:}\\\\\sin^2\theta+\cos^2\theta=1\to\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\\\\\sec\theta=\dfrac{1}{\cos\theta}\\\\==========================\\\\\sin\theta=-\dfrac{5}{7}\\\\\cos\theta=\pm\sqrt{1-\left(-\frac{5}{7}\right)^2}=\pm\sqrt{1-\frac{25}{49}}=\pm\sqrt{\frac{24}{49}}=\pm\dfrac{\sqrt{24}}{\sqrt{49}}=\pm\dfrac{\sqrt{24}}{7}\\\\\sec\theta=\pm\dfrac{1}{\frac{\sqrt{24}}{7}}=\pm\dfrac{7}{\sqrt{24}}

\tan\theta=\pm\dfrac{-\frac{5}{7}}{\frac{\sqrt{24}}{7}}=\mp\dfrac{5}{7\!\!\!\!\diagup_1}\cdot\dfrac{7\!\!\!\!\diagup^1}{\sqrt{24}}=\mp\dfrac{5}{\sqrt{24}}

\sin\theta=-\dfrac{5}{7}

You might be interested in
Help ! determine the coordinates of given point​
Volgvan

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

The coordinates of the marked point is :

  • (0, 9)

7 0
3 years ago
Read 2 more answers
The drama club is showing a video of their recent play. The first showing begins at 4:35 p.M. The second showing is scheduled at
vivado [14]
The video is an hour and ten minutes long.
3 0
3 years ago
Find the measure of an angle whose complement is 20 degrees
PolarNik [594]
It would be 40 becuase if you multiply 20 by 2it gives you 40
4 0
3 years ago
Read 2 more answers
I will really cry if no one helps me
AnnyKZ [126]
True cus I did that before
5 0
3 years ago
Help please urgent please
Oksana_A [137]

Answer:

DEA

Step-by-step explanation:

adjacent is next to and DEA is on line CF with CED

7 0
3 years ago
Other questions:
  • PLEASE ANSWER !! And explain step by step
    10·1 answer
  • Danny and 4 friend go to the movies. Each person buys a movie ticket for $10, a snack for $2 and a drink for $3. Write an expres
    9·1 answer
  • HECTOR PLANTED 185 FLOWERS IN 2 DAYS THERE WERE 5 VOLUNTEERS INCLUDING HECTOR WHO EACH PLANTED ABOUT THE SAME NUMBER OF FLOWERS
    7·1 answer
  • Please help asap!!!
    15·1 answer
  • Need Help ASAP please‼️
    9·1 answer
  • Standard form for 78 hundreds 58 tens 19 ones
    12·1 answer
  • I am an odd number.
    10·2 answers
  • 1) The width of a rectangle is 6 meters less than its length. The area is 315 square meters. Find the length of the
    5·1 answer
  • Which is the solution set of 7y +1> 8y- 9?
    6·1 answer
  • Answer number 1 part b and c please thank you
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!