What is the general solution for 3sin(x+45)=2 ?

The general solution for 3sin(x+45)=2 is x=0.72972…+360n-45,x=180-0.72972…+360n-45

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3sin(x+45)=2

3 sin (x + 4 5^{\circ}) = 2

x = 0.72972 \dots + 36 0^{\circ} n - 4 5^{\circ}, x = 18 0^{\circ} - 0.72972 \dots + 36 0^{\circ} n - 4 5^{\circ}

Solution steps

3 sin (x + 4 5^{\circ}) = 2

Divide both sides by

3

sin (x + 4 5^{\circ}) = \frac{2}{3}

Apply trig inverse properties

x + 4 5^{\circ} = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x + 4 5^{\circ} = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

Solve

x + 4 5^{\circ} = arcsin (\frac{2}{3}) + 36 0^{\circ} n : x = arcsin (\frac{2}{3}) + 36 0^{\circ} n - 4 5^{\circ}

Solve

x + 4 5^{\circ} = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n - 4 5^{\circ}

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n - 4 5^{\circ}, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n - 4 5^{\circ}

Show solutions in decimal form

x = 0.72972 \dots + 36 0^{\circ} n - 4 5^{\circ}, x = 18 0^{\circ} - 0.72972 \dots + 36 0^{\circ} n - 4 5^{\circ}

sin (x) - cos (x) + 1 = 0

cos (8 x) + cos (4 x) = 0

- cot (x) = 0

cos (x) = \frac{3}{10}

cos (θ) + 3 sin (θ) = 1

What is the general solution for 3sin(x+45)=2 ?
The general solution for 3sin(x+45)=2 is x=0.72972…+360n-45,x=180-0.72972…+360n-45