What is the general solution for 7sin(b)=5sin(70) ?

The general solution for 7sin(b)=5sin(70) is b=0.73583…+360n,b=180-0.73583…+360n

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7sin(b)=5sin(70)

7 sin (b) = 5 sin (7 0^{\circ})

b = 0.73583 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.73583 \dots + 36 0^{\circ} n

Radians

b = 0.73583 \dots + 2 πn, b = π - 0.73583 \dots + 2 πn

Solution steps

7 sin (b) = 5 sin (7 0^{\circ})

Divide both sides by

7

7 sin (b) = 5 sin (7 0^{\circ})

Divide both sides by

7

\frac{7 sin ( b )}{7} = \frac{5 sin ( 7 0 ^{\circ} )}{7}

Simplify

sin (b) = \frac{5 sin ( 7 0 ^{\circ} )}{7}

sin (b) = \frac{5 sin ( 7 0 ^{\circ} )}{7}

Apply trig inverse properties

sin (b) = \frac{5 sin ( 7 0 ^{\circ} )}{7}

General solutions for

sin (b) = \frac{5 sin ( 7 0 ^{\circ} )}{7}

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

b = arcsin (\frac{5 sin ( 7 0 ^{\circ} )}{7}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{5 sin ( 7 0 ^{\circ} )}{7}) + 36 0^{\circ} n

b = arcsin (\frac{5 sin ( 7 0 ^{\circ} )}{7}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{5 sin ( 7 0 ^{\circ} )}{7}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.73583 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.73583 \dots + 36 0^{\circ} n

5 sin (x) + 2 cos^{2} (x) = 4

cos (\frac{1}{2} x) = - 1, y = 2

sin^{2} (a) = 2 sin^{2} (a) + 3

cos (x) = \frac{3}{3}, 0 \leq x \leq 2 π

x, y = 2 sec (x)

What is the general solution for 7sin(b)=5sin(70) ?
The general solution for 7sin(b)=5sin(70) is b=0.73583…+360n,b=180-0.73583…+360n