MATH 11TH GRADE HELP

Question

Solve the trigonometric equation for all values? -7< or equal to x < 7

Solve

cot 1/2x -1=0

Answer 1

cot(x/2) = 1

x/2 = 45 degrees +180n where n = any integer = pi/4 + npi where n= any integer

x = 90 degrees = pi/2 + 2npi where n= any integer

cot45 = 1/tan45 = 1/1 = 1

in degrees there is no solution for x which is between -7 and _7

but in radians there is: pi/2 + 2npi where n = an integer which doesn't make pi/2+2npi more than 7 or less than -7 radians. 7 is slightly more than 2pi

-7 < pi/2 + 2npi < +7

n=0, but not 1 or more

n=-1 but not less

n = 0 or -1

pi/2 or pi/2-2pi = -3pi/2

if x=-3pi/2 then x/2 = -3pi/4 radians which is in quadrant III

cot(-3pi/4) = 1

or

cot(-3pi/4) -1 -0

this all assumes you meant (1/2)x and not 1/(2x)?