Question

How do you solve $2\cos x + 4 = 5$ ?

Answer 1

In this question, we are given an equation containing a trigonometric function. The equation is an algebraic expression, as x represents an unknown quantity and the equation is a combination of alphabets and numerical values. To solve this equation, we take all the constant terms on one side of this equation and all the terms containing “x” on the other side. Then we will apply the given arithmetic operation like addition, subtraction, multiplication and division and the rest part of the question can be solved using the knowledge of trigonometry. Trigonometry tells us the relation between the three sides of a right-angled triangle and one of the angles other than the right angle.

Complete step by step answer:
By following the process we will find the solution,
$\Rightarrow 2\cos x + 4 = 5 \\\ \Rightarrow 2\cos x = 5 - 4 \\\ \Rightarrow \cos x = \dfrac{1}{2} \\\$
We know that
$\Rightarrow \cos \dfrac{\pi }{3} = \dfrac{1}{2}$
So, $\cos x = \cos \dfrac{\pi }{3}$
When $\cos a = \cos b$ , we get $a = b$
$\Rightarrow x = \dfrac{\pi }{3}$
Hence, when $2\cos x + 4 = 5$ , we get $x = \dfrac{\pi }{3}$ or $x = 60^\circ$.

Note: Trigonometric functions are of several types – Sine function, cosine function, tangent function, cosecant function, secant function, and cotangent function. Cosecant, secant and cosecant functions are the reciprocal of sine, cosine and tangent functions respectively. We know the value of the trigonometric of some basic angles like $0,\,\dfrac{\pi }{6},\,\dfrac{\pi }{4},\,\dfrac{\pi }{3},\,and\,\dfrac{\pi }{2}$ . We must know the value of these angles to solve similar questions. There are two units to represent angles namely radians and degrees. We know that $\pi$ radians is equal to 180 degrees, using this relation we can convert any angle in radians to degrees as in this question, we have converted $\dfrac{\pi }{3}$ radians into 60 degrees.