Find the GCF of each set of numbers or monomials

Evaluate cosA/2 given cosA=-1/3 and tanA >0

mote1985 [20]

Answer:

$\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}$

Step-by-step explanation:

Given that:

$cosA=-\dfrac{1}3$

and

$tanA > 0$

To find:

$cos\dfrac{A}{2} = ?$

Solution:

First of all,we have cos value as negative and tan value as positive.

It is possible in the 3rd quadrant only.

$\dfrac{A}{2}$ will lie in the 2nd quadrant so $cos\dfrac{A}{2}$ will be negative again.

Because Cosine is positive in 1st and 4th quadrant.

Formula:

$cos2\theta =2cos^2(\theta) - 1$

Here $\theta = \frac{A}{2}$

$cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}$

But as we have discussed, $cos\dfrac{A}{2}$ will be negative.

So, answer is:

$\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}$

7 0

2 years ago

Find the error Hiroshi is finding-15-(-18).Find his mistake and correct it. (-15-(-18)=-15+(-18)=-33

romanna [79]

Answer

he didnt make the 18 positive

Step-by-step explanation:

when u have to negatives u make it a positive

-15 - (-18)

-15+18

3

6 0

3 years ago

15.9 by 9.1 what is the area

Nataliya [291]

Step-by-step explanation:

A = L x W

in multiplication I ignore the decimal points up until I get the answer then add the decimal digits in this case they are two then place the decimal after two digits from the right.

A = 159

x <u> </u><u>91</u>

14469 then place the decimal after two digits from right

= 144.69

6 0

2 years ago

Please help me don’t have that much time please and thank you

dem82 [27]

$f(x)=\frac{1}{9}x-2\\ take:\\x=f(x)^{-1}\\\\f(x)=X\\\\X=\frac{1}{9}f(x)^{-1}-2\\\\(X+2)9 =f(x)^{-1} \\\\f(x)^{-1}=9X+18\\$