What is the general solution for 7sin(a)= 1/11 ?

The general solution for 7sin(a)= 1/11 is a=0.01298…+2pin,a=pi-0.01298…+2pin

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7sin(a)= 1/11

7 sin (a) = \frac{1}{11}

a = 0.01298 \dots + 2 πn, a = π - 0.01298 \dots + 2 πn

Degrees

a = 0.74412 \dots^{\circ} + 36 0^{\circ} n, a = 179.25587 \dots^{\circ} + 36 0^{\circ} n

Solution steps

7 sin (a) = \frac{1}{11}

Divide both sides by

7

7 sin (a) = \frac{1}{11}

Divide both sides by

7

\frac{7 sin ( a )}{7} = \frac{\frac{1}{11}}{7}

Simplify

\frac{7 sin ( a )}{7} = \frac{\frac{1}{11}}{7}

Simplify

\frac{7 sin ( a )}{7} : sin (a)

\frac{7 sin ( a )}{7}

Divide the numbers:

\frac{7}{7} = 1

= sin (a)

Simplify

\frac{\frac{1}{11}}{7} : \frac{1}{77}

\frac{\frac{1}{11}}{7}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{1}{11 \cdot 7}

Multiply the numbers:

11 \cdot 7 = 77

= \frac{1}{77}

sin (a) = \frac{1}{77}

sin (a) = \frac{1}{77}

sin (a) = \frac{1}{77}

Apply trig inverse properties

sin (a) = \frac{1}{77}

General solutions for

sin (a) = \frac{1}{77}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

a = arcsin (\frac{1}{77}) + 2 πn, a = π - arcsin (\frac{1}{77}) + 2 πn

a = arcsin (\frac{1}{77}) + 2 πn, a = π - arcsin (\frac{1}{77}) + 2 πn

Show solutions in decimal form

a = 0.01298 \dots + 2 πn, a = π - 0.01298 \dots + 2 πn

tan (x) = 2, x + y = 135

tan (\frac{x}{2}) + cos (x) = 1

sinh (z) = - 1

1 + cos^{2} (a) = 2 cos^{2} (a)

sin (x) = \frac{15}{18}

What is the general solution for 7sin(a)= 1/11 ?
The general solution for 7sin(a)= 1/11 is a=0.01298…+2pin,a=pi-0.01298…+2pin