What is the general solution for sin(90-θ)=0.5745 ?

The general solution for sin(90-θ)=0.5745 is θ=-360n+90-0.61199…,θ=-180-360n+90+0.61199…

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sin(90-θ)=0.5745

sin (9 0^{\circ} - θ) = 0.5745

θ = - 36 0^{\circ} n + 9 0^{\circ} - 0.61199 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.61199 \dots

Solution steps

sin (9 0^{\circ} - θ) = 0.5745

Apply trig inverse properties

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n, 9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Solve

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n : θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

Solve

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n : θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745), θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

Show solutions in decimal form

θ = - 36 0^{\circ} n + 9 0^{\circ} - 0.61199 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.61199 \dots

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

a, tan (a) = 3

2 cos (12 x) = 3

7 sin (5 x) = 2

arccot (x) + arccot (1 + x) = \frac{π}{4}

What is the general solution for sin(90-θ)=0.5745 ?
The general solution for sin(90-θ)=0.5745 is θ=-360n+90-0.61199…,θ=-180-360n+90+0.61199…