Question

If $\sin x = 0.6$, what is the value of $\cos x$?

Answer 1

In this question we need to use the formula of ${\cos ^2}x + {\sin ^2}x = 1$. With the help of this formula we can find the value of $\cos x$. There can be two values of $\cos x$ one will be positive and other will be negative.

Complete step by step answer:
First, we will think about which formula we can use in this question which has a relation between $\cos x$ and $\sin x$,and then we will proceed further.
Here we can use the formula ${\cos ^2}x + {\sin ^2}x = 1$ to solve this question further.
Therefore,
${\cos ^2}x + {\sin ^2}x = 1$
Now substitute the value of $\sin x = 0.6$ in the above equation.
$\Rightarrow {\cos ^2}x + {\left( {0.6} \right)^2} = 1$
We know that the value of ${\left( {0.6} \right)^2} = 0.36$.
Therefore,
$\Rightarrow {\cos ^2}x + 0.36 = 1$
Now transposing $0.36$ to the right-hand side.
$\Rightarrow {\cos ^2}x = 1 - 0.36$
Now taking root on both the sides,
$\Rightarrow \cos x = \pm \sqrt {1 - 0.36}$
$\Rightarrow \cos x = \pm \sqrt {0.64}$
Now, we know that the root of $\sqrt {0.64}$is $0.8$.
$\Rightarrow \cos x = \pm 0.8$
Therefore, there are two values of $\cos x$ are $+ 0.8$ ,$- 0.8$.

Additional information: In Trigonometry, different types of problems can be solved using trigonometry formulas. These problems may include trigonometric ratios (sin, cos, tan, sec, cosec and cot), Pythagorean identities, product identities, etc. Some formulas include the sign of ratios in different quadrants, involving co-function identities (shifting angles), sum & difference identities, double angle identities, half-angle identities, etc.

Note: There are several identities which make relations between $\sin x$ and $\cos x$ . But the identity which we have used above is the easiest one to calculate and it also takes less time to reach the answer.