Question

How to solve trig equations?

Answer 1

Hint: The trigonometric equations are the equations which involves one or more of the six functions such as sine, cosine, tangent secant and cosecant. The trigonometric equations can be solved by using or following the algorithms.

Complete step by step solution:
To solve trigonometric equations, follow the below given steps for the quick and accurate solutions –
i.First of all take one function of the one angle. Just like any equations trigonometric ii.equations are really all about the numbers and not the angles.
iii.Then start solving for the values of the trigonometric functions.
iv.Then solve for the angle and lastly for the variable
v.Apply any restrictions applicable since when you convert the cosine into sine be careful about the sign convention.
Also remember the All STC rule, it is also known as ASTC rule in geometry. It states that all the trigonometric ratios in the first quadrant ( $ 0^\circ \;{\text{to 90}}^\circ $ ) are positive, sine and cosec are positive in the second quadrant ( $ 90^\circ {\text{ to 180}}^\circ $ ), tan and cot are positive in the third quadrant ( $ 180^\circ \;{\text{to 270}}^\circ $ ) and sin and cosec are positive in the fourth quadrant ( $ 270^\circ {\text{ to 360}}^\circ $ ).

Note: Every point on the circle is unit circle from the origin. So, the coordinates of any point are within one of zero as well. Directly the Pythagoras identity is followed by sines and cosines which concludes that $ si{n^2}\theta + co{s^2}\theta = 1 $ . Always remember the correlation between the six trigonometric functions for replacing the given function and forming the equivalent equation for the efficient and an accurate solution.