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
Anuta_ua [19.1K]
3 years ago
15

Sandra knows the Pythagorean identity sin 2 ⁡ θ + cos 2 ⁡ θ = 1 . If she is told that 0 ≤ θ ≤ π 2 and cos ⁡ θ = 5 12, what will

she get when she correctly calculates tan ⁡ θ ?
Mathematics
1 answer:
slavikrds [6]3 years ago
5 0

Answer:

\text{tan}(\theta)=\frac{\sqrt{119}}{5}

Step-by-step explanation:

We have been given that Sandra knows the Pythagorean identity \text{sin}^2(\theta)+\text{cos}^2(\theta)=1. She is told that 0\leq \theta\leq \frac{\pi}{2} and \text{cos}(\theta)=\frac{5}{12}.

First of all, we will find value of sine theta using the given identity.

\text{sin}^2(\theta)+\text{cos}^2(\theta)=1

\text{sin}^2(\theta)+(\frac{5}{12})^2=1

\text{sin}^2(\theta)+\frac{25}{144}=1

\text{sin}^2(\theta)+\frac{25}{144}-\frac{25}{144}=1-\frac{25}{144}

\text{sin}^2(\theta)=\frac{144-25}{144}

\text{sin}^2(\theta)=\frac{119}{144}

\text{sin}(\theta)=\sqrt{\frac{119}{144}}

\text{sin}(\theta)=\frac{\sqrt{119}}{12}  

\text{tan}(\theta)=\frac{\text{sin}(\theta)}{\text{cos}(\theta)}

\text{tan}(\theta)=\frac{\frac{\sqrt{119}}{12}}{\frac{5}{12}}

\text{tan}(\theta)=\frac{\sqrt{119}*12}{5*12}=\frac{\sqrt{119}}{5}

Therefore, \text{tan}(\theta)=\frac{\sqrt{119}}{5}.

You might be interested in
Factor the expression.
tiny-mole [99]
B. (k+10f)(k-5f) you can tell in 2 ways.  1. if the second sign is neg then the signs in the factors are going to be one neg and one positive so that knocks out C and D.  Then you look at the second term and since the 5 is positive then the 10 has to be positive so you end up with a positive 5kf.

The second way is to FOIL them out.  When you check B you get k^{2} -5kf+10kf- 50f^{2} combine your like terms and you have your original expression of k^{2} +5kf-50 f^{2}

Hope that helps
3 0
3 years ago
What is x? 30=5(z+1)
Troyanec [42]

Answer: 5

B/c 5+1= 6 and 5 times 6 is 30

5 0
3 years ago
The function g(x) = -2x + 3. Compare the slopes and y-intercepts. A. Both the slopes and the y-intercepts are different. B. Both
Brums [2.3K]

Answer:

both the slopes and the y intercepts are the same for both of these functions because if you look at the graph you will notice that the y intercept is positive 3 just the function and to get its slope just use the formula y2-y1/x2-x1 to get the slope of also a -2 so answer is b

5 0
2 years ago
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Strike441 [17]

I hope this is right

220.5 cubic feet

3 0
3 years ago
Help Please 20 points and Brainliest if the answer is Correct!!!!! ( Do not put a random answer or I will report)
Firdavs [7]

Answer:

k^2/25

Step-by-step explanation:

(1/5k)^2

(k/5)^2

k^2/5^2

k^2/25

6 0
2 years ago
Read 2 more answers
Other questions:
  • Passing through (2, - 2) and perpendicular to the line whose equation is y= 5x+2
    7·1 answer
  • The moon is about 240,000 miles from Earth what is the distance written as a whole number multipled by the power of ten?
    8·2 answers
  • What is the area of the rectangle?
    15·2 answers
  • Sketch the figure: Two different isosceles triangles with perimeter 4a + b
    6·1 answer
  • 3 1/2 divided by 2 1/4 in simplest form?<br><br> 3 1/2 divided by 1/4?
    8·2 answers
  • Find numerator that makes statement true? 2/4 is less than /6
    7·1 answer
  • Last week Jason had 43 dollars. He washed cars over the weekend and
    7·1 answer
  • a train covers a distance at an average speed of 60km / hr in 12 hours. what should be the speed of the train if the same distan
    15·1 answer
  • What does an individual's effective tax rate indicate?
    11·2 answers
  • If sin(theta)=0.7 what is tan(theta)?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!