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
Leya [2.2K]
3 years ago
15

Given that sin theta = 1/4, 0

Mathematics
1 answer:
GaryK [48]3 years ago
6 0
Answer: cos(Θ) = (√15) / 4

Explanation:

The question states:

1) sin(Θ) = 1/4

2) 0 < Θ < π / 2

3) find cos(Θ)

This is how you solve it.

1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

(cos \alpha )^2 + (sin \alpha )^2 =1

2) From which you can find:

(cos \alpha )^2 = 1 - (sin \alpha )^2

3) Replace sin(α) with 1/4

=> (cos \alpha )^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16

=> cos \alpha =+/- \sqrt{15/16} = +/- (\sqrt{15} )/4

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:

cos(Θ) = \sqrt{15} /4.

And that is the answer.
You might be interested in
What<br> percent of 150 is 225?
likoan [24]

Answer:

150%

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Which of the following geometric series converges?
Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}

Multiply both sides by <em>r</em> :

rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n

Subtract the latter sum from the first, which eliminates all but the first and last terms:

S_n-rS_n=a-ar^n

Solve for S_n:

(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}

Then as gets arbitrarily large, the term r^n will converge to 0, leaving us with

S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0
2 years ago
Match each graph with its corresponding equation
s344n2d4d5 [400]
The equation of the parabolas given will be found as follows:
a] general form of the parabolas is:
y=k(ax^2+bx+c)
taking to points form the first graph say (2,-2) (3,2), thus
y=k(x-2)(x-3)
y=k(x^2-5x+6)

taking another point (-1,5) 
5=k((-1)^2-5(-1)+6)
5=k(1+5+6)
5=12k
k=5/12
thus the equation will be:
y=5/12(x^2-5x+6)

b] Using the vertex form of the quadratic equations:
y=a(x-h)^2+k
where (h,k) is the vertex
from the graph, the vertex is hence: (-2,1)
thus the equation will be:
y=a(x+2)^2+1
taking the point say (0,3) and solving for a
3=a(0+2)^2+1
3=4a+1
a=1/2
hence the equation will be:
y=1/2(x+2)^2+1


5 0
3 years ago
7x + y = 7<br> y = [ ? ]x+ []
otez555 [7]
Y=-7x+7

hope this helped!
6 0
3 years ago
This is the full question
alexdok [17]
The answer appears to be 2 dollars for 3 pounds because the pattern seems like 2,4,6
4 0
3 years ago
Read 2 more answers
Other questions:
  • 15 POINTSPLEASE HELP WITH MY MATH PROBLEM
    12·1 answer
  • Mr. Rawlings had 60 cookies he wanted to give each of his 16 grandchildren the same number of cookies what is the greatest numbe
    6·1 answer
  • How many tennis balls do you need to balance to scale
    13·2 answers
  • 85% of the people survey thought the price of the car wash was reasonable. If 164 people thought the cost of the car wash was re
    15·1 answer
  • Billie and toni are driving from chicago to phoenix. the first day they drove 420 miles. they want to drive at 65 miles per hour
    5·1 answer
  • PLEASE HELP! 20 POINTS!An equation was created for the line of best fit from the actual enrollment data. It was used to predict
    6·2 answers
  • how is x &gt; 4(with a dash under the symbol in the middle,symbol is not on my keyboard)graphed on a number line?​
    6·1 answer
  • Solve for x4:=(-8)+3x
    7·1 answer
  • 5 + 0.55x = 10 + 0.75x pls help and explain ​
    15·2 answers
  • CAN SOMEONE HELP PLZZZZ ALGEBRA
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!