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
daser333 [38]
3 years ago
7

What is the exact value of cos112.5?

Mathematics
2 answers:
Harrizon [31]3 years ago
5 0
The answer is -0.382683432 if 112.5 is in degrees
quester [9]3 years ago
4 0

The exact value of cos⁡ 112.5 is \bold{-\frac{\sqrt{(2-\sqrt{2})}}{2}= 0.3827531}

<u>Solution:</u>

Use half angle formula for Cos,

\begin{array}{l}{\cos \left(\frac{x}{2}\right)=\pm \sqrt{\frac{1+\cos x}{2}}} \\ {\cos 112.5=\cos \frac{225}{2}=-\sqrt{\frac{1+\cos 225}{2}} \quad(\text { equation } 1)}\end{array}

(Since cos 112.5 is in II quadrant ,negative sign is used)            

cos⁡  225 = cos⁡ (45+180)

cos ⁡(a+b) = cos a cos b+sin a sin⁡ b

cos ⁡(45+180) = cos 45 cos⁡ 180+ sin⁡ 45 sin ⁡180

\begin{array}{l}{\cos 45=\frac{\sqrt{2}}{2}} \\ \\ {\sin 45=\frac{\sqrt{2}}{2}}\end{array}

cos⁡ 180 = -1  

sin⁡ 180 = 0

\begin{array}{l}{\cos (45+180)=\frac{\sqrt{2}}{2}(-1)+\frac{\sqrt{2}}{2}(0)} \\\\ {\cos (45+180)=-\frac{\sqrt{2}}{2}+0} \\\\ {\cos (45+180)=-\frac{\sqrt{2}}{2}(\text { equation } 2)}\end{array}

apply equation 2 in equation 1

\begin{array}{l}{\cos \frac{225}{2}=-\sqrt{\frac{1+\left(-\frac{\sqrt{2}}{2}\right)}{2}}=-\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}}=-\sqrt{\frac{2-\sqrt{2}}{2}}=-\sqrt{\frac{2-\sqrt{2}}{4}}} \\ {\cos \frac{225}{2}=-\frac{\sqrt{2-\sqrt{2}}}{2}} \\ {\cos 112.5=-\frac{\sqrt{2-\sqrt{2}}}{2}}=0.3827531\end{array}

You might be interested in
Write the slope-intercept form of the equation of the line that passes through the point (-4,0 ), and is parallel to y=-(5/4x)+4
amid [387]

Answer:

Step-by-step explanation:

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1)   when : x_1= -4      y_1= 0  

     m= +5/4 (parallel means same slope)

an equation in the point-slope form is : y +0= -5/4(x+4)

4 0
2 years ago
Please help me with part b of this question. THanks.
nevsk [136]
Ur image is kinda cut off
"on the diagram aboe to what point does each point below correspond when t"
then nothing
<span />
8 0
3 years ago
Answer quickly please
adell [148]

Answer:

A C E

Step-by-step explanation:

pls mark brainliest

8 0
2 years ago
IM GIVING BRAINLIEST!!!PLEASE HELP!!!I JUST KNOW ITS NOT A!!!
zmey [24]

Answer:

C. In y^2-y=6, 6 should have been subtracted on both sides first.

Step-by-step explanation:

It is a quadratic equation so you subtract the 6 and create

y^2-y-6=0

Then you factor it to:

(y-3)(y+2)=0

The solutions then are:

y-3=0, y=3 and y+2=0, y=-2

{-2,3}

4 0
3 years ago
Solve.<br> x^2+9x+2=0<br> thanks!
shtirl [24]
Step one:
ALWAYS set equation equal to zero, which in this case has already been done for us.

Step two:
Figure out what formula you need to use in order to solve in this case I'd use the Quadratic formula.

a=1
b=9
c=2

Quadratic formula:
x =  \frac{ - b +  -  \sqrt{(b) ^{2}  - 4(a)(c)} }{2(a)}
Then you would plug in the information.
x = \frac{ - 9+  -  \sqrt{(9) {}^{2} - 4(1)(2) } }{2(1)}
The solve for what is underneath the square root ONLY.
x =  \frac{ - 9 +  -  \sqrt{73} }{2}
Since you cannot solve this any further, your final two answers are...
x =   \frac{ - 9 +  \sqrt{73} }{2}
x =   \frac{ - 9 -  \sqrt{73} }{2}






3 0
3 years ago
Other questions:
  • Solve the following simultaneous equations : with the help of steps<br>1. x + 2y = 1, 3x - y = 17​
    14·1 answer
  • 30 tens minus 3 tens 3 tenths
    14·1 answer
  • I don't get this please can someone solve/ help me with this appreciate it thank you
    5·1 answer
  • How do you get the answer for 10x4= _ x 5
    9·2 answers
  • Mr Thompson had a balance of $283.12 in his checking account at the beginning of the month he wrote checks for $203.09, $7.56, $
    13·2 answers
  • If the base area of a cone is 78.5 square centimeters and the height
    12·1 answer
  • What roles did African American men take on during the war? Check all of the boxes that apply They worked as cooks. They enliste
    12·2 answers
  • [-1 + (-4)] + (6/7 + 1/7)
    5·1 answer
  • PLEASE HELP I WILL GIVE BRAINLIEST
    10·1 answer
  • 1. Camille received $1000 in graduation gifts. He found a savings plan that will pay him 4% interest compounded continuously. Us
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!