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

√7/3.

Step-by-step explanation:

csc Ø = 1 / sin Ø =  1 / -4/3 = -3/4.

As the sine is the opposite / hypotenuse  the side adjacent to angle Ø  will have length √(4^2 - 3^2) = √7 (by the Pythagoras theorem) and as  the angle is in the third quadrant this will be -√7.

So cot Ø = adjacent / opposite =  -√7/ -3

= √7/3   (answer).

Step-by-step explanation:

It is given that cosec =-4/3 and sin theta =1/cosec theta

so sin theta =-3/4 now since sin theta is perpendicular/hypotenuse, the third side base will be

and we know that cot theta is inverse of tan so it will be base/perpendicular

i.e and also it is given that side of theta is in quadrant III so cot theta will be positive, so final answer will be

answer: i believe it’s 245.04

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for