Question

The general value of \[\theta \] satisfying \[sin2\theta + sin\theta = 2\]
A. \[n\pi + ( - 1)n\pi /6\]
B. \[2n\pi + \pi /4\]
C. \[n\pi + ( - 1)n\pi /2\]
D. \[n\pi + ( - 1)n\pi /3\]

Answer 1

Hint:
 The most common value of is \[{\bf{\theta }} = {\bf{n}}{\rm{ }}{\bf{\pi }} + {\bf{\alpha }}\;\], obeying the equations \[sin{\rm{ }}\theta {\rm{ }} = {\rm{ }}sin{\rm{ }}\alpha \]and \[cos{\rm{ }}\theta {\rm{ }} = {\rm{ }}cos{\rm{ }}\alpha \].Finding all possible sets of values for that satisfy the given equation is the goal when attempting to solve a trigonometric problem. When an equation's graph can be easily drawn and the equation is simple,

Complete step by step solution: \[sin2\theta + sin\theta = 2\]
⟹\[sin\theta = 2 - 1 \pm 9 = - 2,{\bf{1}}\]
⟹\[sin\theta = - 2\;or\;sin\theta = 1\]
⟹\[\theta = n\pi + ( - 1)n2\pi \]
To stay competitive in the exams, students are urged to understand all of the trigonometric formulas, including the trigonometry fundamentals. To become familiar with the subject, students should practice a variety of trigonometry problems based on trigonometric ratios and the fundamentals of trigonometry.
 If \[tan{\rm{ }}\theta \] or \[sec{\rm{ }}\theta \] is involved in the equation, \[\theta {\rm{ }} \ne \]odd multiple of \[\pi /2\].
 If \[cot{\rm{ }}\theta \] or \[cosec{\rm{ }}\theta \] is involved in the equation, \[\theta {\rm{ }} \ne \]multiple of \[\pi \] or\[0\].
The y-value of point P on the unit circle represents the sine of the angle. Therefore, we indicate the two equal intervals in the graph since \[sin\theta {\rm{ }} = {\rm{ }}sin{\rm{ }}\left( {180 - \theta {\rm{ }}} \right).\]As a result, the graph is approximately \[90^\circ \] symmetric between \[0^\circ \]and \[180^\circ \]. Similarly, the graph is symmetric around \[270^\circ \]between \[180^\circ \] and \[360^\circ .\] A circle with a radius of one is referred to as a unit circle. The unit circle is frequently the circle with radius \[1\] that is centered at the origin, especially in trigonometry \[\left( {0,{\rm{ }}0} \right)\].

 Option ‘C’ is correct

Note: There isn't a single way to solve trigonometric equations that can be defined. In each situation, the ability to solve a trigonometric equation successfully depends in part on the understanding and practical application of the trigonometric formula as well as problem-solving experience. For many trigonometric formulas, all of the values of the variables that appear in them are true equivalences.