2q,b ii) $$ \sin 20=0,64 $$ vi) $$ 3-3 \cos 20=2,28 $$. 3. If $$ 2 an \left(x+53^{\circ} ight)=-1,26 $$, calculate solution

Question

2q,b ii) $$ \sin 20=0,64 $$ vi) $$ 3-3 \cos 20=2,28 $$. 3. If $$ 2 	an \left(x+53^{\circ}ight)=-1,26 $$, calculate solution

UpStudy AI · Accepted Answer

1. Divide the equation by 2:
  
   $$
   2 \tan\left(x+53^\circ\right)=-1.26 \quad \Rightarrow \quad \tan\left(x+53^\circ\right)=-0.63.
   $$

2. Write the general solution for a tangent equation. Since the period of the tangent function is $$180^\circ$$, we have

$$
   x+53^\circ=\arctan(-0.63)+180^\circ \cdot k,\quad k\in\mathbb{Z}.
   $$

3. Compute the principal value:
  
   $$
   \arctan(-0.63)\approx -32^\circ.
   $$

4. Substitute the principal value:

$$
   x+53^\circ\approx -32^\circ+180^\circ\cdot k.
   $$

5. Solve for $$x$$:

$$
   x\approx -32^\circ-53^\circ+180^\circ\cdot k=-85^\circ+180^\circ\cdot k,\quad k\in\mathbb{Z}.
   $$

Thus, the solutions are:

$$
x=-85^\circ+180^\circ\cdot k,\quad k\in\mathbb{Z}.
$$
The solutions are $$ x = -85^\circ + 180^\circ \times k $$, where $$ k $$ is any integer.

2q,b ii) \( \sin 20=0,64 \) vi) \( 3-3 \cos 20=2,28 \). 3. If \( 2 \tan \left(x+53^{\circ}\right)=-1,26 \), calculate solution