Need help with some trig questions?

Question

can someone please show me how to find these?

1. Use half-angle formulas to find the exact value for cot 75°

2. Find all x and y between 0 and 2π so that the equation is true
-2 cos x - i sin y = 2 sin x + i

3. Show that x = 6+2i is a solution to the equation x² - 12x + 40 = 0

Answer 1

dont have much time and see nobody has responded

#3 use quadratic equation (-b +or- sqrt (b^2-4ac))/2a

note: equation must be in form of ax^2 +bx +c = 0 which yours is.

thus: a =1, b=-12, and c= 40

(-(-12)+or- sqrt(144-160))/2

= (12+or-(sqrt -16))/2
= (12 +or- (sqrt -16))2
= (12 +or- 4i)/2
= 6 +or- 2i so 6 + 2i and 6-2i are the solutions

hope this helps
you may want to submit a & b; better to do one at a time

Answer 2

#1
I can help you with the first question.
if you have ur book find the half-angle formulas and plug them in. here's the formula that I found.
(sinx)^2=(1-cos2x)/2 and (cos x)^2=(1+cos2x)/2
that's the formulas that I perfer to use.
since you need to find "cot 75degree" and the half angle formula only has "sine and cosine" you need to replace cot having sine or cosine or both so that you can plug it into the formula...and change degree to radian also.

here's a trick that I always remember...refering to triangle
y=height/how tall x=weight/how long r=the *hypos/always the longest leg from the rest.
sine=y/r <---> csc=r/y
cos=x/r <---> sec=r/x
tan=y/x <---> cot=x/y
always remember the three important one first which is sine, cosine, and tan...and you'll know the other three left. sine and csc they just flip...and as to the rest also.

cot 75 change it to radian as in pie.
to find the radian when there's a degree always use "pie/180"
75/1 = pie/180 cross multiply and you'll get "5pie/12"

now that it's in radian form...you need to find the half angle for both sine and cosine first to be able to slove for cot...since cot is equal to x/y....and sine is the y and cos is the x...

after you have found sine5pie/12 and co5pie/12....then use the half angle again to plug in:
cot 5pie/12 which is (cos5pie/12)/(sin5pie/12)
ur answer well mostly be in radical since the half angle is squared.

good luck...hope I made myself clear and sorry for the pie thing...i can't find pie in my computer like urs.