SOLUTION: Hi,
I'm very lost. The direction said to find the exact value of Θ in the interval of 0˚≤ Θ ≤ 360˚ that satisfy each equation.
1)csc^2 Θ
Algebra ->
Trigonometry-basics
-> SOLUTION: Hi,
I'm very lost. The direction said to find the exact value of Θ in the interval of 0˚≤ Θ ≤ 360˚ that satisfy each equation.
1)csc^2 Θ
Log On
Question 1029714: Hi,
I'm very lost. The direction said to find the exact value of Θ in the interval of 0˚≤ Θ ≤ 360˚ that satisfy each equation.
1)csc^2 Θ-cot Θ -1=0 ( this is cosecant squared theta minus cotangent theta minus 1 =0)
this is what I did so far: (1/sin^2 Θ) - (cosΘ /sinΘ) -1=0
then multiplied by sinΘ and from there I got confused because when I got my final answer:Θ does not exist, it didn't match the answer given.
2)2cosΘ =secΘ
3)cot^2 Θ =cscΘ +1 (this is cotangent squared theta = cosecant theta plus 1)
for all of these questions my final answers don't match the answers that were given I tried solving another way but I'm stuck. can you please help me Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! find the exact value of Θ in the interval of 0˚≤ Θ ≤ 360˚ that satisfy each equation.
1)csc^2 Θ-cot Θ -1=0
-----
(cot^2+1) - cot - 1 = 0
cot^2(t) - cot(t) = 0
cot(cot-1) = 0
cot(t) = 0 or cot(t) = 1
------
t = pi/2 or (3/2)pi or pi/4 or (5/4)pi
================================================
2)2cosΘ =secΘ
2cos(t) = 1/cos(t)
cos^2(t) = 1/2
----
cos(t) = 1/sqrt(2)
t = +/-(pi/3)
---------
3)cot^2 Θ =cscΘ +1
-----
(csc^2 - 1) = csc + 1
----
csc^2 - csc -2 = 0
-----
(csc-2)(csc+1) = 0
------------------
csc(t) = 2 or csc(t) = -1
-----------------------
t = pi/6 or (5/6)pi or (3/2)pi
--------------------------
Cheers,
Stan H.
--------------
(