1/(1.5)=(sin(30))/(sin(x)),x<90

Solution

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

x = 0.84806 \dots, x = - 5.43512 \dots, x = - 18 0^{\circ} - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

Solution steps

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

Switch sides

\frac{sin ( 3 0 ^{\circ} )}{sin ( x )} = \frac{1}{1.5}

sin (3 0^{\circ}) = \frac{1}{2}

\frac{\frac{1}{2}}{sin ( x )} = \frac{1}{1.5}

Cross multiply

1.5 = 2 sin (x)

Switch sides

2 sin (x) = 1.5

Divide both sides by

2

sin (x) = 0.75

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = 0.75

Apply trig inverse properties

x = arcsin (0.75) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75) + 36 0^{\circ} n

Solutions for the range

x < 9 0^{\circ}

x = 0.84806 \dots, x = - 5.43512 \dots, x = - 18 0^{\circ} - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

tan (A) = \frac{8}{15}

tan^{2} (θ) = sec^{2} (θ) + 1

cos (2 B) = \frac{21}{35}, cos (B)

2 cos^{4} (x) + 3 sin^{2} (x) - 2 = 0

cos^{2} (x) + 4 sin^{2} (\frac{x}{2}) = 1