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Popular >

sin(θ)-cos(θ)=sqrt((2+\sqrt{3))/2}

Solution

sin (θ) - cos (θ) = \frac{2 + 3}{2}

Solution

θ = 1.30899 \dots + 2 πn + \frac{π}{4}, θ = π - 1.30899 \dots + 2 πn + \frac{π}{4}

+1

Solution steps

sin (θ) - cos (θ) = \frac{2 + 3}{2}

Rewrite using trig identities

2 sin (θ - \frac{π}{4}) = \frac{2 + 3}{2}

Divide both sides by

2

sin (θ - \frac{π}{4}) = \frac{2 + 3}{2}

Apply trig inverse properties

θ - \frac{π}{4} = arcsin (\frac{2 + 3}{2}) + 2 πn, θ - \frac{π}{4} = π - arcsin (\frac{2 + 3}{2}) + 2 πn

Solve

θ - \frac{π}{4} = arcsin (\frac{2 + 3}{2}) + 2 πn : θ = arcsin (\frac{2 + 3}{2}) + 2 πn + \frac{π}{4}

Solve

θ - \frac{π}{4} = π - arcsin (\frac{2 + 3}{2}) + 2 πn : θ = π - arcsin (\frac{2 + 3}{2}) + 2 πn + \frac{π}{4}

θ = arcsin (\frac{2 + 3}{2}) + 2 πn + \frac{π}{4}, θ = π - arcsin (\frac{2 + 3}{2}) + 2 πn + \frac{π}{4}

Show solutions in decimal form

θ = 1.30899 \dots + 2 πn + \frac{π}{4}, θ = π - 1.30899 \dots + 2 πn + \frac{π}{4}

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