prove sin(θ)=-5/12

Solution

prove

sin (θ) = - \frac{5}{12}

False

Solution steps

sin (θ) = - \frac{5}{12}

Show that the two sides are not equal

For

sin (θ) = - \frac{5}{12}

plug in

θ = 0

sin (0) = 0

sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0

The two sides are not equal

\Rightarrow False

tan (\frac{π}{3}) = 3

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

sec (0) sin (0) = tan (0)

sec (x) = \frac{tan ( x )}{sin ( x )}

tan^{2} (x) = \frac{sec ^{2} ( x )}{csc ^{2} ( x )}