Find the exact value of cot theta if csc theta = -4/3 and the terminal side of theta lies in quadrant iii.

The exact value of cotФ  is    

Step-by-step explanation:

Given as:

The value of cosec Ф =

Let the value of  cotФ = x

Now, According to question

∵  sinФ =                       .....1

Put the value of cosec Ф = in eq 1

i.e  sinФ =

Or,  sinФ =

Again

∵ cosФ =

So,  cosФ =

Or, cosФ =

Or,  cosФ =

∴  cosФ =

Again

we know that cotФ =

So,  cotФ  =

Or,  cotФ  =

As according to question sinФ lies in third quadrant

So,  cotФ  =  

Hence, The exact value of cotФ  is     . Answer

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

idk

step-by-step explanation: