What is the general solution for sin(x)=-0.978 ?

The general solution for sin(x)=-0.978 is x=-1.36064…+2pin,x=pi+1.36064…+2pin

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sin(x)=-0.978

sin (x) = - 0.978

x = - 1.36064 \dots + 2 πn, x = π + 1.36064 \dots + 2 πn

Degrees

x = - 77.95939 \dots^{\circ} + 36 0^{\circ} n, x = 257.95939 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - 0.978

Apply trig inverse properties

sin (x) = - 0.978

General solutions for

sin (x) = - 0.978

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

x = arcsin (- 0.978) + 2 πn, x = π + arcsin (0.978) + 2 πn

x = arcsin (- 0.978) + 2 πn, x = π + arcsin (0.978) + 2 πn

Show solutions in decimal form

x = - 1.36064 \dots + 2 πn, x = π + 1.36064 \dots + 2 πn

cos (t) = \frac{15}{17}

cos (x) = - \frac{3}{2 3}

sec^{2} (x) - 6 sec (x) = 16

cos^{2} (θ) + sin^{2} (θ) = 4

6 arccos (x) - 3 π = 3 arccos (x)

What is the general solution for sin(x)=-0.978 ?
The general solution for sin(x)=-0.978 is x=-1.36064…+2pin,x=pi+1.36064…+2pin