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
nydimaria [60]
1 year ago
12

Given sin⁡θ=1/2 determine the value of sec θ. 0°<θ<90°

Mathematics
1 answer:
Alika [10]1 year ago
8 0

By applying the concepts of <em>trigonometric</em> functions and given that sin θ = 1/2 and 0° < θ < 90°, then the value of the secant of the given angle is \frac{2\sqrt{3}}{3}. (Right choice: A)

<h3>How to determine the exact value of a given trigonometric function based on a known value</h3>

By trigonometry, we understand that the sine is defined by the following function:

\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}      (1)

Where:

  • y - Opposite leg
  • x - Adjacent leg

And the function secant is defined by:

\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}     (2)

If we know that x² + y² = 4 and y = 1, then we find that the secant is:

x² + 1 = 4

x² = 3

x = \sqrt{3}

Secant is postive for 0° < θ < 90°, thus:

\sec \theta = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}

By applying the concepts of <em>trigonometric</em> functions and given that sin θ = 1/2 and 0° < θ < 90°, then the value of the secant of the given angle is \frac{2\sqrt{3}}{3}. (Right choice: A)

To learn more on trigonometric functions: brainly.com/question/6904750

#SPJ1

You might be interested in
1+1 abcdefghijklmnopqrstuvwxyandz
skad [1K]

Answer:2


Step-by-step explanation: two 1 equal one 2


3 0
2 years ago
Read 2 more answers
The sum of three consecutive even integers is 102. Find the largest of the three integers.
marissa [1.9K]

Answer to the question is..

32,34,36

largest is 36

7 0
3 years ago
Evaluate C = 2 r, for r = 8.
Jet001 [13]

Answer:

C = 16

Step-by-step explanation:

Substitute r = 8 into the equation for C, hence

C = 2r = 2 × 8 = 16

4 0
2 years ago
Read 2 more answers
Simplify quantity 1 minus cosine squared theta divided by sine squared theta..
Ulleksa [173]
For this case we have the following fraction:
 (1-cos ^ 2 (θ)) / (sin ^ 2 (θ))
 We must take into account the following trigonometric identity:
 cos ^ 2 (θ) + sin ^ 2 (θ) = 1
 Therefore rewriting we have:
 sin ^ 2 (θ) = 1 - cos ^ 2 (θ)
 Substituting in the given fraction we have:
 (1-cos ^ 2 (θ)) / (sin ^ 2 (θ))
 = (sin ^ 2 (θ)) / (sin ^ 2 (θ))
 = 1
 Answer:
 
1
4 0
3 years ago
Solve the system x-y=5 and 4x-5y+17
Goshia [24]

Answer:

Step-by-step explanation:

x = 3

7=2

3-2=5

slope is 4/5

8 0
2 years ago
Other questions:
  • Shelly states that the triangles below are similar. Which proportion supports her statement?
    8·2 answers
  • Two people independently each pick a number from 1 to 10. what is the probability that the two of them pick the same number?
    10·1 answer
  • What is the slope of (2 , -2) (0,4)
    9·2 answers
  • Let z= -5 sqrt 3/2 + 5/2i and w=1 + sqrt 3i
    7·1 answer
  • Use the binomial squares pattern to multiply (7c²+6)²
    9·1 answer
  • 2(x + 4) - 5 = 3x + 3
    13·2 answers
  • You have been tracking how much you spend on gas every month for several months and found that on average you spend about $60 pe
    10·1 answer
  • The freezing point of a certain liquid is -7F . Another liquid freezes at -12F . What is the difference between the absolute val
    10·1 answer
  • The table shows a function. Is the function linear or nonlinear?​
    14·1 answer
  • What angles are Adjacent to angle 4 below?​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!