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
Phoenix [80]
3 years ago
11

Find cos θ given that cos 2θ = 5/6 and 0 ≤ θ < π/2. Give an exact answer

Mathematics
1 answer:
trasher [3.6K]3 years ago
3 0
\bf \textit{Double Angle Identities}&#10;\\ \quad \\&#10;sin(2\theta)=2sin(\theta)cos(\theta)&#10;\\ \quad \\&#10;cos(2\theta)=&#10;\begin{cases}&#10;cos^2(\theta)-sin^2(\theta)\\&#10;1-2sin^2(\theta)\\&#10;\boxed{2cos^2(\theta)-1}&#10;\end{cases}&#10;\\ \quad \\&#10;tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\&#10;-------------------------------\\\\&#10;

\bf cos(2\theta)=\cfrac{5}{6}\implies 2cos^2(\theta)-1=\cfrac{5}{6}\implies 2cos^2(\theta)=\cfrac{5}{6}+1&#10;\\\\\\&#10;2cos^2(\theta)=\cfrac{11}{6}\implies cos^2(\theta)=\cfrac{11}{12}\implies cos(\theta)=\pm\sqrt{\cfrac{11}{12}}


now, bear in mind, the square root gives us +/- versions, so, which is it? well, we know the angle is in the range of "<span>0 ≤ θ < π/2", that simply means the 1st quadrant, so, we'll use the positive one then

</span>\bf cos(\theta)=\cfrac{\sqrt{11}}{\sqrt{12}}\implies cos(\theta)=\cfrac{\sqrt{11}}{2\sqrt{3}}&#10;\\\\\\&#10;\textit{now, let's rationalize the denominator}&#10;\\\\\\&#10;\cfrac{\sqrt{11}}{2\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{\sqrt{11}\cdot \sqrt{3}}{2\sqrt{3^2}}\implies \cfrac{\sqrt{11\cdot 33}}{2\cdot 3}\implies \boxed{\cfrac{\sqrt{33}}{6}}<span>
</span>
You might be interested in
What is measure of angle R?
Oliga [24]
Angle R can be solved using the inverse sine button on a calculator. Sine is y/r so opposite leg over the hypotenuse. For r, the opposite leg is 5cm and the hypotenuse is 13. The inverse sin button looks like sin^-1. Punch that in the calculator (make sure in degree mode). Punch the inverse sin and then 5/13 and you should get 22.62°
4 0
3 years ago
CHECK Mynicknameisnickname THEY HAVE THIS QUESTION FOR 100 POINTS FOR THE FIRST CORRECT PERSON HURRY!!
mars1129 [50]
Let "c" and "q" represent the numbers of bottles of Classic and Quantum that should be produced each day to maximize profit. The problem conditions give rise to 3 inequalities:
.. 0.500c +0.550q ≤ 100 . . . . . . . liters of water
.. 0.600c +0.200q ≤ 100 . . . . . . . kg of sugar
.. 0.1c +0.2q ≤ 32 . . . . . . . . . . . . . grams of caramel
These can be plotted on a graph to find the feasible region where c and q satisfy all constraints. You find that the caramel constraint does not come into play. The graph below has c plotted on the horizontal axis and q plotted on the vertical axis.

Optimum production occurs near c = 152.17 and q = 43.48. Examination of profit figures for solutions near those values reveals the best result for (c, q) = (153, 41). Those levels of production give a profit of 6899p per day.


To maximize profit, Cartesian Cola should produce each day
.. 153 bottles of Classic
.. 41 bottles of Quantum per day.

Profit will be 6899p per day.


_____
The problem statement gives no clue as to the currency equivalent of 100p.

5 0
3 years ago
A squirrel runs at a steady rate of 0.51 m/s in a circular path around a tree. If the squirrel's centripetal acceleration is 0.4
exis [7]
The image is answer.................

4 0
3 years ago
Read 2 more answers
−6x+14&lt;−28 OR 9x+15≤−12
Serhud [2]

Answer:x>7 or x ≤ -3

Solving the 1st inequality

-6x +14 < -28 --------------- (Collect like terms)

-6x < -28 - 14

-6x < - 42 -------------------- (Divide both sides by -6)

Note: If you decide an inequality expression by a negative value, the inequality sign changes)

-6x/-6 > -42/-6

x > 7

Solving the 2nd inequality

9x + 15 ≤ −12 ----------- (Collect like terms)

9x ≤ −12 - 15

9x ≤ −27 ------------------(Divide both sides by 9)

9

9x/9 ≤ −27/9

x ≤ -3

Bring both results together, we get

x>7 or x ≤ -3

The final result is complex (i.e. can't be combined together).

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
In a certain state, car license plates are numbered in the form of LL NNNN, where L stands for a letter of the alphabet and N st
Rashid [163]
L=26
N=10
So it's 26*26*10*10*10*10=6760000
8 0
3 years ago
Read 2 more answers
Other questions:
  • The results from the last quiz that Mr. Tham gave his class are 10, 15, 25, 75, 75, 77, 80, 83, 85, and 90. Which statistical me
    9·2 answers
  • Use the graph of f to estimate the local maximum and local minimum. A cubic graph is shown increasing, then decreasing, then inc
    8·1 answer
  • What is 4 divided by 100
    12·2 answers
  • My question is, with this type of question, are you supposed to use subtraction instead of addition? Just asking because I had a
    10·2 answers
  • Graph each function. y= -x2 + 5 (the -x is squared, to the second power, so it's -x to the second power
    9·1 answer
  • What is the answer to this question
    14·2 answers
  • Select all the rates that are unit rates.<br><br> 1 1/3 <br> 2 3/1<br> 2/3<br> 3/1<br> 1/9
    14·2 answers
  • A plumber charges $15 for transportation and $40 per hour for repairs complete the expression that can be used to find the cost
    10·1 answer
  • How much will 28 pencils cost if 7 pencils cost $1.82?
    11·2 answers
  • 9. Chocolate Co. mixes two kinds of chocolate bars
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!