What is the general solution for sin(2x)=cos(40) ?

The general solution for sin(2x)=cos(40) is x=(900+6480n)/(36),x=(2340+6480n)/(36)

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sin(2x)=cos(40)

sin (2 x) = cos (4 0^{\circ})

x = \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{36}, x = \frac{234 0 ^{\circ} + 648 0 ^{\circ} n}{36}

Solution steps

sin (2 x) = cos (4 0^{\circ})

Rewrite using trig identities

sin (2 x) = sin (9 0^{\circ} - 4 0^{\circ})

Apply trig inverse properties

2 x = 9 0^{\circ} - 4 0^{\circ} + 36 0^{\circ} n, 2 x = 18 0^{\circ} - (9 0^{\circ} - 4 0^{\circ}) + 36 0^{\circ} n

2 x = 9 0^{\circ} - 4 0^{\circ} + 36 0^{\circ} n : x = \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{36}

2 x = 18 0^{\circ} - (9 0^{\circ} - 4 0^{\circ}) + 36 0^{\circ} n : x = \frac{234 0 ^{\circ} + 648 0 ^{\circ} n}{36}

x = \frac{90 0 ^{\circ} + 648 0 ^{\circ} n}{36}, x = \frac{234 0 ^{\circ} + 648 0 ^{\circ} n}{36}

- 15 sin (x) - 8 cos (x) = 10

- 5 sec^{2} (x) + 20 = 0

1 + cos (x) = 3 \cdot sin (x)

4 sin (θ) = 2 (1 + sin (θ))

sinh (y) = 2

What is the general solution for sin(2x)=cos(40) ?
The general solution for sin(2x)=cos(40) is x=(900+6480n)/(36),x=(2340+6480n)/(36)