last one,how do you prove this ?
(cotX + cosecX)^2 = 1+cosX/1-cosX
some people are just born to fail maths
hi, i have this HW for my class assessment mark so i really want to get it all perfect, its some tedious work, but help is greatly appreciated.Thanks in advance. pls help me check if i made any mistakes in my calculations
1) solve 5sinX - 2cos^2X - 1 = 0 range(for 0 <= x <= 2pie) <= is great equal sign
i worked out and got sinX = 1/2 and sinX = -3
for sin = 1/2 converting to degress(using calculator inverse sin) is 30,
using quadrant diagram x1 = 30 degrees
x2 = 180-30 = 150
sinx = -3 is undefined? though i don't know if i did any mistake in my previous calculations
btw if the range is given in terms of pie, does the teacher expects the answer to be given in terms of pie?, i can't figure out what 150 is in terms of pie
2) sec^2X - 4tanX = 0 for (0<= x <= 180)
using identities sec^2X = tan^2X +1 thus
tan^2 X - 4tan X +1 = 0
since it can't be factored mentally , i used the quadratic equation to factor
got tan X = 3.732
using calculator inverse tan and quadrant diagram got
X1 = 75
x2 = 180 + 75 = 255
(all in terms of degees)
next tanX = 0.268
using above methods got X1= 15.5
X2 = 180 - 15.5 = 164.5
3) 3sinX = 5sinXcosX (for -90 <x<90)
completely lost, tried diveding everything by cosX, didn't work
and where do i start of finish in the quadrant diagram if its -90
4) 3 sinX = 5sinXcosX (for -90<x<90)
got 3/5 = cosx
inverse of cos 3/5 = 53.1(degrees)
stuck on the quadrant diagram, becasue of the range.
help is greatly appreciated, i tried, just got stuck on some, and its a very important piece of HW