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
kumpel [21]
3 years ago
9

HELP! Find the value of sin 0 if tan 0 = 4; 180 < 0< 270

Mathematics
1 answer:
BabaBlast [244]3 years ago
4 0

Hi there! Use the following identities below to help with your problem.

\large \boxed{sin \theta = tan \theta cos \theta} \\  \large \boxed{tan^{2}  \theta + 1 =  {sec}^{2} \theta}

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

\large{ {4}^{2}  + 1 =  {sec}^{2} \theta } \\  \large{16 + 1 =  {sec}^{2} \theta } \\  \large{ {sec}^{2}  \theta = 17}

As we know, sec²θ = 1/cos²θ.

\large \boxed{sec \theta =   \frac{1}{cos \theta} } \\  \large \boxed{ {sec}^{2}  \theta =  \frac{1}{ {cos}^{2}  \theta} }

And thus,

\large{  {cos}^{2}  \theta =  \frac{1}{17}}   \\ \large{cos \theta =  \frac{ \sqrt{1} }{ \sqrt{17} } } \\  \large{cos \theta =  \frac{1}{ \sqrt{17} }  \longrightarrow  \frac{ \sqrt{17} }{17} }

Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.

\large{cos \theta =   \cancel\frac{ \sqrt{17} }{17} \longrightarrow cos \theta =  -  \frac{ \sqrt{17} }{17}}

Then use the Identity of sinθ = tanθcosθ to find the sinθ.

\large{sin \theta = 4 \times ( -  \frac{ \sqrt{17} }{17}) } \\  \large{sin \theta =  -  \frac{4 \sqrt{17} }{17} }

Answer

  • sinθ = -4sqrt(17)/17 or A choice.
You might be interested in
Help please :( points !
mars1129 [50]
Answer: 2/5

Explanation: 10+8+12 = 30 12/30 = .4 .4 = 2/5
4 0
3 years ago
Read 2 more answers
Help with this question please
Maru [420]

Answer:

I don't know so sorry!

5 0
3 years ago
5,111 ÷ 3 it wont show up on calculator
Mashcka [7]

Answer:

Step-by-step explanation:

In calculator the answer is 1703.66666667

3 0
3 years ago
Read 2 more answers
What is the largest prime factor of 12
Alex Ar [27]

Answer:

3

Step-by-step explanation:


8 0
3 years ago
Read 2 more answers
Solve the equation. If the equation is an identity, choose identity. If it has no solution, choose no solution. 4(t + 2) = 10
Nuetrik [128]

Answer & Step-by-step explanation:

4(t + 2) = 10

4t + 8 = 10

4t = 2

t = 1/2

Hope this helps

3 0
3 years ago
Other questions:
  • Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!
    10·2 answers
  • True or False?<br> k = 3 over 5 is a solution to the inequality 15k + 3 &lt; 15.
    8·2 answers
  • What is the distance between E(-7, 8) and F(1, -6)? leave in simplified radical form
    5·1 answer
  • Find the hcf of 144 and 180. if it is expressed in the form 13m-3, find the value of m​
    5·2 answers
  • If y=2x+10 and X= -2 then what is y
    8·2 answers
  • A certain electronics manufacturer found that the average cost C C to produce x DVD/Blu- ray players can be found using the equa
    6·1 answer
  • the doctor recommended that Matt increase the number of calories he consumed from 2000 to 2800. By what percent did the number o
    13·1 answer
  • BRAINLIEST!URGENT! Someone said that its B. but never gave me the steps. Can someone please show me how the answer is B?​
    10·1 answer
  • When x 4, y = 1<br> х^2 + Зry — 7у^2<br><br><br> Can you explain the whole answer.
    8·1 answer
  • Manny borrowed $800 at 10% annual interest. How much interest did he owe in one year?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!