Solve For Θ
0 ≤ Θ < 360
sin θ + 1 / sin θ = 2
sin ² θ + 1 = 2 sin θ
sin ² θ - 2 sin θ + 1 = 0
(sin θ - 1) (sin θ - 1) = 0
sin θ = 1
θ = 90°
sinÎ + cscÎ = 2
sinÎ + 1/sinÎ = 2
sin²Π+ 1/sinΠ= 2
sin²Î+ 1 = 2 sinÎ
sin²Π- 2sinΠ+ 1 = 0
(sinÎ-1)² = 0
(sinÎ-1) = 0
sinÎ= 1
sinÎ = 90 deg and its positive and negative multiples. pi/2 is the radian equivalent
First write the equivalent of CscÎ,
That is 1/sinÎ ,then we have:
sinÎ+1/sinÎ=2
[(sinÎ)^2+1]/sinÎ=2 ;
(sinÎ)^2+1=2sinÎ
use this formula : (a-b)^2=a^2+b^2-2ab
so you have:
(sinÎ-1)^2=0 ;
sinÎ=1
Î=2k(pi) +pi/2 and Î=2k(pi)+(pi)-(pi)/2 = 2k(pi)+(pi)/2
considering 0 ⤠Π< 360 we have:
Î=pi/2 or Î=90
x is easier to type than Î. so
sin x + 1/sin x = 2
sin² x + 1 = 2sin x
sin² - 2sin + 1 = 0
(sin - 1)² = 0
sin x = 1
x = 90°
Csc t = 1 / sin t right?
so...
Sin t + Csc t = Sin t + 1 / Sin t
Solve for Sin t, as if (sin t) were a single variable, you can rewrite it as x+ 1/x = 2, if that helps. (x = sin t).
When you know sin t, you can solve that on a calculater easily.
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Verified answer
sin θ + 1 / sin θ = 2
sin ² θ + 1 = 2 sin θ
sin ² θ - 2 sin θ + 1 = 0
(sin θ - 1) (sin θ - 1) = 0
sin θ = 1
θ = 90°
sinÎ + cscÎ = 2
sinÎ + 1/sinÎ = 2
sin²Π+ 1/sinΠ= 2
sin²Î+ 1 = 2 sinÎ
sin²Π- 2sinΠ+ 1 = 0
(sinÎ-1)² = 0
(sinÎ-1) = 0
sinÎ= 1
sinÎ = 90 deg and its positive and negative multiples. pi/2 is the radian equivalent
First write the equivalent of CscÎ,
That is 1/sinÎ ,then we have:
sinÎ+1/sinÎ=2
[(sinÎ)^2+1]/sinÎ=2 ;
(sinÎ)^2+1=2sinÎ
use this formula : (a-b)^2=a^2+b^2-2ab
so you have:
(sinÎ-1)^2=0 ;
sinÎ=1
Î=2k(pi) +pi/2 and Î=2k(pi)+(pi)-(pi)/2 = 2k(pi)+(pi)/2
considering 0 ⤠Π< 360 we have:
Î=pi/2 or Î=90
x is easier to type than Î. so
sin x + 1/sin x = 2
sin² x + 1 = 2sin x
sin² - 2sin + 1 = 0
(sin - 1)² = 0
sin x = 1
x = 90°
Csc t = 1 / sin t right?
so...
Sin t + Csc t = Sin t + 1 / Sin t
Solve for Sin t, as if (sin t) were a single variable, you can rewrite it as x+ 1/x = 2, if that helps. (x = sin t).
When you know sin t, you can solve that on a calculater easily.