enable's commence by keeping apart the cosecant: ?3 csc? - 2 = 0 ?3 csc? = 2 csc? = (2/?3) If the question replaced into inquiring for tangent, sine, or cosine, you may might want to rationalize the denominator, yet because csc is an identical as a million/sin, you may in basic terms turn the fraction and remedy for sine: a million/sin = (2/?3) sin? = (?3/2) The reference attitude with the sine of ?3/2 is 60 ranges, or ?/3. keep in mind that there are diverse angles with a similar sine. Sine is sensible contained in the first and 2d quadrants, so the 2d attitude degree may be one hundred twenty ranges, or 2?/3. i'm hoping this helps!
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Secθ+√2=0
Cosθ = -1 / √2
θ = 3π/4 + 2kπ, where k is any integer.
or
θ=3π/4+2kπ,k ∈Z)
enable's commence by keeping apart the cosecant: ?3 csc? - 2 = 0 ?3 csc? = 2 csc? = (2/?3) If the question replaced into inquiring for tangent, sine, or cosine, you may might want to rationalize the denominator, yet because csc is an identical as a million/sin, you may in basic terms turn the fraction and remedy for sine: a million/sin = (2/?3) sin? = (?3/2) The reference attitude with the sine of ?3/2 is 60 ranges, or ?/3. keep in mind that there are diverse angles with a similar sine. Sine is sensible contained in the first and 2d quadrants, so the 2d attitude degree may be one hundred twenty ranges, or 2?/3. i'm hoping this helps!
sec θ = -sqrt(2)
cos θ = -1 / sqrt(2) = -sqrt(2) / 2 ==>
θ = 3pi/4 + 2pi * k or θ = 5pi/4 + 2pi * k
(this will be a 45-45-90 triangle in Q2 and Q3, since sec and cos are < 0 when x < 0)