SinΘ + CscΘ = 2?

Question

Solve For Θ

0 ≤ Θ < 360

Answer 1

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°

Answer 2

sinΘ + cscΘ = 2
sinΘ + 1/sinΘ = 2
sin²Θ + 1/sinΘ = 2
sin²Θ+ 1 = 2 sinΘ
sin²Θ - 2sinΘ + 1 = 0
(sinΘ-1)² = 0
(sinΘ-1) = 0
sinΘ= 1
sinΘ = 90 deg and its positive and negative multiples. pi/2 is the radian equivalent

Answer 3

First write the equivalent of CscΘ,
That is 1/sinΘ ,then we have:
sinΘ+1/sinΘ=2
[(sinΘ)^2+1]/sinΘ=2 ;

(sinΘ)^2+1=2sinΘ
use this formula : (a-b)^2=a^2+b^2-2ab
so you have:
(sinΘ-1)^2=0 ;
sinΘ=1

Θ=2k(pi) +pi/2 and Θ=2k(pi)+(pi)-(pi)/2 = 2k(pi)+(pi)/2

considering 0 ≤ Θ < 360 we have:
Θ=pi/2 or Θ=90

Answer 4

x is easier to type than Θ. 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°

Answer 5

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.