What is the general solution for sin(x)=-8/17 ,pi<= x<= (3pi)/2 ,sin(2x) ?

The general solution for sin(x)=-8/17 ,pi<= x<= (3pi)/2 ,sin(2x) is x=pi+0.48995…

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sin(x)=-8/17 ,pi<= x<= (3pi)/2 ,sin(2x)

sin (x) = - \frac{8}{17}, π \leq x \leq \frac{3 π}{2}, sin (2 x)

x = π + 0.48995 \dots

Degrees

x = 208.07248 \dots^{\circ}

Solution steps

sin (x) = - \frac{8}{17}, π \leq x \leq \frac{3 π}{2}, sin (2 x)

Apply trig inverse properties

sin (x) = - \frac{8}{17}

General solutions for

sin (x) = - \frac{8}{17}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{8}{17}) + 2 πn, x = π + arcsin (\frac{8}{17}) + 2 πn

x = arcsin (- \frac{8}{17}) + 2 πn, x = π + arcsin (\frac{8}{17}) + 2 πn

Solutions for the range

π \leq x \leq \frac{3 π}{2}

x = π + arcsin (\frac{8}{17})

Show solutions in decimal form

x = π + 0.48995 \dots

tan (θ) cos (2 7^{\circ}) = cos (6 3^{\circ})

3 - sin (x) = cos (2 x)

cot^{2} (x) - cot (x) - 2 = 0

cos^{2} (θ) = 0.1831

tan (a + 5^{\circ}) = 2 sin (3 0^{\circ}) + sec (24 5^{\circ})

What is the general solution for sin(x)=-8/17 ,pi<= x<= (3pi)/2 ,sin(2x) ?
The general solution for sin(x)=-8/17 ,pi<= x<= (3pi)/2 ,sin(2x) is x=pi+0.48995…