(368.02)/(sin(66-x))=(290)/(sin(38))

Solution

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

x = - 36 0^{\circ} n + 6 6^{\circ} - 0.89673 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + 0.89673 \dots

Solution steps

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

Cross multiply

368.02 sin (3 8^{\circ}) = sin (6 6^{\circ} - x) \cdot 290

Switch sides

sin (6 6^{\circ} - x) \cdot 290 = 368.02 sin (3 8^{\circ})

Divide both sides by

290

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Verify Solutions

Find undefined (singularity) points:

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

Combine undefined points with solutions:

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Apply trig inverse properties

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n, 6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

Solve

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n : x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

Solve

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n : x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}), x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

Show solutions in decimal form

x = - 36 0^{\circ} n + 6 6^{\circ} - 0.89673 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + 0.89673 \dots

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

tan (x) = \frac{9.3}{7.5}

sin (α) + cos (α) = 1

2 sin (θ) = 3 tan (θ)

sin (x^{2} - 1) = 4