Solving trigonometric equations is all about finding the x value in the equation, or what may be also known as the angle in the equation.
First things first, to be able to solve trigonometric equations, you must first master your special angles and must know it by heart. refer to previous posts if you need kick-start reviews on special angles
Step by Step:
1. Simplify the equation so the left hand side has only the trigonometric identity and right hand side has only the integers
2. Note the positive/negative sign on the right hand side. Then determine which quadrant the angle is in (with reference to the trigonometric identity on the left hand side)
3. Find the value/s of x (note that the value of x determined from the equation is an acute angle. Thus, the possible values of x must be determined by adding or substracting angles to the acute angle, depending on which quadrant the angle is in)
e.g.
sin x = - s.r3 / 2 ; 0 < x < 2pi
Since we know that the acute angle of x is pi / 3 (use special angles to determine the angle in pink), and now after sketching the graph, we know that sin x lies in the 3rd and 4th quadrant (because in the 3rd and 4th quadrant, sin is a negative ; this matches with the answer determined). Hence, there are 2 values of x which lie in the 3rd and 4th quadrant (obeying the restriction that x's maximum is 2pi)
x = pi / 3 + pi >>> because to find an angle in the 3rd quadrant is pi + acute angle
= 4pi / 3
AND
x = 2pi - pi / 3
= 5pi / 3
Solving trigonometric identities is really about practising by doing more exercises and familiarizing yourself with the special angles and methods to solve it.
Definitely not a one-time-go math topic.
Check this video out. It'll probably help you understand the above much, much better.
Good Luck!
First things first, to be able to solve trigonometric equations, you must first master your special angles and must know it by heart. refer to previous posts if you need kick-start reviews on special angles
Step by Step:
1. Simplify the equation so the left hand side has only the trigonometric identity and right hand side has only the integers
2. Note the positive/negative sign on the right hand side. Then determine which quadrant the angle is in (with reference to the trigonometric identity on the left hand side)
3. Find the value/s of x (note that the value of x determined from the equation is an acute angle. Thus, the possible values of x must be determined by adding or substracting angles to the acute angle, depending on which quadrant the angle is in)
e.g.
sin x = - s.r3 / 2 ; 0 < x < 2pi
x = pi / 3 + pi >>> because to find an angle in the 3rd quadrant is pi + acute angle
= 4pi / 3
AND
x = 2pi - pi / 3
= 5pi / 3
Solving trigonometric identities is really about practising by doing more exercises and familiarizing yourself with the special angles and methods to solve it.
Definitely not a one-time-go math topic.
Check this video out. It'll probably help you understand the above much, much better.
Good Luck!
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