What is the general solution for (26)/(sin(88))=(21)/(sin(c)) ?

The general solution for (26)/(sin(88))=(21)/(sin(c)) is c=0.93939…+360n,c=180-0.93939…+360n

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(26)/(sin(88))=(21)/(sin(c))

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

c = 0.93939 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.93939 \dots + 36 0^{\circ} n

Radians

c = 0.93939 \dots + 2 πn, c = π - 0.93939 \dots + 2 πn

Solution steps

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

Cross multiply

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

26 sin (c) = sin (8 8^{\circ}) \cdot 21

26 sin (c) = sin (8 8^{\circ}) \cdot 21

Divide both sides by

26

26 sin (c) = sin (8 8^{\circ}) \cdot 21

Divide both sides by

26

\frac{26 sin ( c )}{26} = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

Simplify

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

Verify Solutions

Find undefined (singularity) points:

sin (c) = 0

Take the denominator(s) of

\frac{21}{sin ( c )}

and compare to zero

sin (c) = 0

The following points are undefined

sin (c) = 0

Combine undefined points with solutions:

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

Apply trig inverse properties

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

General solutions for

sin (c) = \frac{sin ( 8 8 ^{\circ} ) 21}{26}

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

c = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n

c = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n

Show solutions in decimal form

c = 0.93939 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.93939 \dots + 36 0^{\circ} n

3 tan^{2} (3 x) = 1

- 2 (cos (2 x) + sin (x)) = 0

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

6 tan (x) - 5 csc (x) = 0

2 (19) tan (\frac{θ}{2}) = 6.3

What is the general solution for (26)/(sin(88))=(21)/(sin(c)) ?
The general solution for (26)/(sin(88))=(21)/(sin(c)) is c=0.93939…+360n,c=180-0.93939…+360n