What is the general solution for sin(x)=0.707 ?

The general solution for sin(x)=0.707 is x=0.78524…+2pin,x=pi-0.78524…+2pin

sin(x)=0.707

sin (x) = 0.707

x = 0.78524 \dots + 2 πn, x = π - 0.78524 \dots + 2 πn

Degrees

x = 44.99134 \dots^{\circ} + 36 0^{\circ} n, x = 135.00865 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.707

Apply trig inverse properties

sin (x) = 0.707

General solutions for

sin (x) = 0.707

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

x = arcsin (0.707) + 2 πn, x = π - arcsin (0.707) + 2 πn

x = arcsin (0.707) + 2 πn, x = π - arcsin (0.707) + 2 πn

Show solutions in decimal form

x = 0.78524 \dots + 2 πn, x = π - 0.78524 \dots + 2 πn

cos (θ) = \frac{4 2}{7}, sin (θ)

arctan (\frac{1}{x - 1}) + arctan (\frac{2}{x + 1}) = \frac{π}{4}

cot (3 x) = - tan (- \frac{2 π}{5})

cos (x) = \frac{60}{61}

cot (x) = 2

What is the general solution for sin(x)=0.707 ?
The general solution for sin(x)=0.707 is x=0.78524…+2pin,x=pi-0.78524…+2pin