What is the general solution for sin(90-a)= 1/(1.63) ?

The general solution for sin(90-a)= 1/(1.63) is a=-360n+90-0.66048…,a=-180-360n+90+0.66048…

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sin(90-a)= 1/(1.63)

sin (9 0^{\circ} - a) = \frac{1}{1.63}

a = - 36 0^{\circ} n + 9 0^{\circ} - 0.66048 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.66048 \dots

Solution steps

sin (9 0^{\circ} - a) = \frac{1}{1.63}

Apply trig inverse properties

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n, 9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

Solve

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n : a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

Solve

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n : a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63}), a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

Show solutions in decimal form

a = - 36 0^{\circ} n + 9 0^{\circ} - 0.66048 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.66048 \dots

cot^{2} (x) - cos^{2} (x) = - 1

sin^{2} (θ) = 2 \cdot sin (θ) + 3

tan (3 x) = 1, - 2 π \leq x \leq 2 π

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

cos (x) sin (2 x) + 3 sin^{2} (x) = - 3 sin (x)

What is the general solution for sin(90-a)= 1/(1.63) ?
The general solution for sin(90-a)= 1/(1.63) is a=-360n+90-0.66048…,a=-180-360n+90+0.66048…