What is the general solution for sin(60-a)=0.598 ?

The general solution for sin(60-a)=0.598 is a=-360n+60-0.64100…,a=-180-360n+60+0.64100…

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sin(60-a)=0.598

sin (6 0^{\circ} - a) = 0.598

a = - 36 0^{\circ} n + 6 0^{\circ} - 0.64100 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + 0.64100 \dots

Solution steps

sin (6 0^{\circ} - a) = 0.598

Apply trig inverse properties

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n, 6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n

Solve

6 0^{\circ} - a = arcsin (0.598) + 36 0^{\circ} n : a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598)

Solve

6 0^{\circ} - a = 18 0^{\circ} - arcsin (0.598) + 36 0^{\circ} n : a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

a = - 36 0^{\circ} n + 6 0^{\circ} - arcsin (0.598), a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + arcsin (0.598)

Show solutions in decimal form

a = - 36 0^{\circ} n + 6 0^{\circ} - 0.64100 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 6 0^{\circ} + 0.64100 \dots

sin (a) = 0.143

sin (x) = cos^{2} (x) + 1

sin (a) = 1.25

(1 + \frac{tan ^{2} ( a )}{1} + cot^{2} (a)) = tan^{2} (a)

2 cos (x) + 1 = sin^{2} (x)

What is the general solution for sin(60-a)=0.598 ?
The general solution for sin(60-a)=0.598 is a=-360n+60-0.64100…,a=-180-360n+60+0.64100…