What is the general solution for sin(x-30)=0.7 ?

The general solution for sin(x-30)=0.7 is x=0.77539…+360n+30,x=180-0.77539…+360n+30

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sin(x-30)=0.7

sin (x - 3 0^{\circ}) = 0.7

x = 0.77539 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 0.77539 \dots + 36 0^{\circ} n + 3 0^{\circ}

Radians

x = 0.77539 \dots + \frac{π}{6} + 2 πn, x = π - 0.77539 \dots + \frac{π}{6} + 2 πn

Solution steps

sin (x - 3 0^{\circ}) = 0.7

Apply trig inverse properties

sin (x - 3 0^{\circ}) = 0.7

General solutions for

sin (x - 3 0^{\circ}) = 0.7

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (0.7) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (0.7) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n

Solve

x - 3 0^{\circ} = arcsin (0.7) + 36 0^{\circ} n : x = arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = arcsin (0.7) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = arcsin (0.7) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

Solve

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - arcsin (0.7) + 36 0^{\circ} n + 3 0^{\circ}

Show solutions in decimal form

x = 0.77539 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 0.77539 \dots + 36 0^{\circ} n + 3 0^{\circ}

\leq 3 \cdot cos (x) - sin (x) = 0

tan^{2} (x) + sec^{2} (x) = 3

4 sin^{2} (x) - 6 cos^{2} (x) = 0

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

sin (a) = 0.143

What is the general solution for sin(x-30)=0.7 ?
The general solution for sin(x-30)=0.7 is x=0.77539…+360n+30,x=180-0.77539…+360n+30