prove sin(θ)=0.2

Solution

prove

sin (θ) = 0.2

False

Solution steps

sin (θ) = 0.2

Show that the two sides are not equal

For

sin (θ) = 0.2

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

\frac{cos ( 4 t ) - cos ( 2 t )}{sin ( 4 t ) + sin ( 2 t )} = - tan (t)

sec (2 x) = \frac{csc ( x )}{csc ( x ) - 2 sin ( x )}

(1 - cos^{2} (θ)) (csc^{2} (θ)) = 1

\frac{1}{arctan ( x )} = arccot (x)

\frac{1}{sin ( θ ) cos ( θ )} - tan (θ) = cot (θ)