√2 CSCꝊ - 2=0 ...

Question

Solve for if 0° ≤ 𝜃 < 360

Answer 1

Hello Maya,

Assuming your equation is square_root(2) * csc(x) -2 =0:

Add 2 to both sides: square_root(2)* csc(x) = 2

Divide both sides by square_root(2): csc(x) = 2/square_root(2) ----> csc(x) = square_root(2)

Write csc(x) as 1/sin(x): 1/sin(x) = square_root(2)

Cross-multiply: sin(x) *square_root(2) = 1

Divide by square_root(2) on both sides: sin(x) = 1/square_root(2) = square_root(2)/2

Now you have the equation: sin(x) = square_root(2)/2

Which angles on the unit circle have a sine equal to √(2)/2 ?

(Hint 1: There should only be 2 angles)

(Hint 2: sin(x) is positive in quadrant 1 and quadrant 2, so you want to look for your solutions there)

(Hint 3: the solution in quadrant 1 is 45 degrees.)

45 and the 2nd angle you find will be the solutions to the equation.

Cheers.