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
vekshin1
3 years ago
9

Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )

Mathematics
1 answer:
Zina [86]3 years ago
8 0

Answer:

\purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

Step-by-step explanation:

\cos( \alpha ) =  \frac{ \sqrt{6} }{6}  =  \frac{1}{ \sqrt{6} }  \\  \\  \therefore \:  \sin( \alpha )  =  \sqrt{1 -  { \cos}^{2} ( \alpha ) }  \\  \\  =  \sqrt{1 -  \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} }  \\  \\ =  \sqrt{1 -  {\frac{1}{ {6} }}}  \\  \\ =  \sqrt{ {\frac{6 - 1}{ {6} }}}   \\  \\  \red{\sin( \alpha ) =  \sqrt{ { \frac{5}{ {6} }}} } \\  \\  \tan( \alpha ) =  \frac{\sin( \alpha ) }{\cos( \alpha ) }  =  \sqrt{5}  \\  \\ \sin( \beta )  =  \frac{ \sqrt{2} }{4}  \\  \\  \implies \: \cos( \beta )  =   \sqrt{ \frac{7}{8} }  \\  \\ \tan( \beta )  =  \frac{\sin( \beta ) }{\cos( \beta ) } =  \frac{1}{ \sqrt{7} }   \\  \\  \tan( \alpha  -  \beta ) =  \frac{ \tan \alpha  -  \tan \beta }{1 +  \tan \alpha .  \tan \beta}  \\  \\  =  \frac{ \sqrt{5} -  \frac{1}{ \sqrt{7} }  }{1 +  \sqrt{5} . \frac{1}{ \sqrt{7} } }  \\  \\  =  \frac{ \sqrt{35} - 1 }{ \sqrt{7}  +  \sqrt{5} }  \\  \\  \purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

You might be interested in
Beth is making fruit salad. She adds 3 grapes for every 2 strawberries. If she uses 16 strawberries, how many grapes will she us
yaroslaw [1]

The amount of grapes that she would need is 32 grapes.

6 0
3 years ago
Read 2 more answers
A certain town never has two sunny days in a row. Each day is classified as being either sunny, cloudy (but dry), or rainy. If i
11111nata11111 [884]

Answer:

the proportion of days that are Sunny is 0.2

Step-by-step explanation:

Given the data in the question;

Using markov chain;

3 states; Sunny(1), Cloudy(2) and Rainy(3)

Now, based on given conditions, the transition matrix can be obtained in the following way;

\left[\begin{array}{ccc}0&0.5&0.5\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]

so let the proportion of sunny, cloudy and rainy days be S, C and R respectively.

such that, from column 1

S = 0.25C + 0.25R   -------------let this be equation 1

from column 2

0.5C = 0.5S + 0.25R

divided through by 0.5

C = S + 0.5R ---------------------- let this be equation 2

now putting equation 2 into equation;

S = 0.25(S + 0.5R) + 0.25R

S = 0.25S + 0.125R + 0.25R

S - 0.25S = 0.375R

0.75S = 0.375R

S = 0.375R / 0.75

S = 0.5R

Therefore,

from equation 2; C = S + 0.5R

input S = 0.5R

C = 0.5R + 0.5R

C = R

Now, we know that, the sum of the three proportion should be equal to one;

so

S + C + R = 1

since C = R and S = 0.5R

we substitute

0.5R + R + R = 1

2.5R = 1

R = 1/2.5

R = 0.4

Hence, the proportion of days that are Rainy is 0.4

C = R

C = 0.4

Hence, the proportion of days that are Cloudy is 0.4

S = 0.5R

S = 0.5(0.4)

S = 0.2

Hence, the proportion of days that are Sunny is 0.2

8 0
3 years ago
Simplify Rewrite the expression in the form x ^ n X^ 2 * x ^ - 12 =
Natalija [7]

Step-by-step explanation:

Given

=  {x}^{2} \times  {x}^{ - 12 } \\  =  {x}^{2 - 12}    \\  =  {x}^{ - 10}

Hope it will help :)

8 0
3 years ago
Read 2 more answers
Is y=7x-3 have a proportional relationship
Black_prince [1.1K]

Answer:

my name is mmmmmmm

Step-by-step explanation:

hehehehe

8 0
3 years ago
A.)12 <br> B.) 25<br> C.)51<br> D.) 77
givi [52]

Answer:

4x+3=2x+27

4x-2x=27-3

2x=24

x=24/2

x=12

3 0
2 years ago
Read 2 more answers
Other questions:
  • Assume that the two polygons are similiar, with the same orientation.
    8·1 answer
  • A bell tolls every 10 minutes. Another bell tolls every 15 minutes. Both bells toll at 6:00 PM. They will toll together again at
    11·2 answers
  • What is the least common multiple of 16, 6, and 12?
    15·2 answers
  • PLEASE HELP !!
    9·1 answer
  • What is the answer for -7 = 6-1/5x
    9·1 answer
  • Susan has 3 shirts ; red, blue, and green; jeans and khakis; and 3 shoes; white, black, and tan , to choose from for her school
    7·1 answer
  • For the right triangle shown, use the trig functions to find the value of x. Round your answer to the nearest tenth.
    9·1 answer
  • A box contains 14 large marbles and 11 small marbles. Each marble is either green or white. 8 of the large marbles are green, an
    7·1 answer
  • Solve the answer <br> 6p - 1 - 4p = 15?
    12·1 answer
  • Need help on this question thank you!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!