help on part b, please <@&791435371564892232>
#year 13 trigonometry
unique stump
unique stump
<@&791435371564892232>
obtuse mica
Let 4theta + 10degrees = 2x
if we look at what we are given in part a
we know that cosec2x + cot2x = cotx
hence cosec(4theta + 10) + cot(4theta + 10) = cot(2theta+5)
hence we can rewrite our equation as:
cot(2theta + 5 degrees) = sqrt(3)
cot = 1/tan(angle)
hence 1/tan(2theta + 5 degrees) = sqrt(3)
hence 1/sqrt(3) = tan(2theta+5)
arctan(1/sqrt3) = 30, 210 (although 210 is more than 180 we will still test to see if theta is less than 180)
our first equation will be 30 = 2theta + 5 hence theta = 12.5
our second equation will be (210 -5)/2 =102.5 = theta
if we want to test another value
just add 180 to 210 (period of tan)
390 = 2theta + 5
hence 385/2 = theta
sadly this is 192.5 which is out our range
no need to test any values less than 30 because they will be negative (-150) which will give us a negative theta which we dont want
rustic fjord
bro absolutely cooked