Question

How do you calculate $\cos A=0.81$ ?

Answer 1

In the given question we are required to find the value of the angle $A$ , so that we can get the value of $\cos A=0.81$ . To solve this, we just simply have to take the inverse of $\cos$ function and equate it to the value $0.81\;$

Complete step-by-step answer:
Given:
$\cos A=0.81$ To find the value of the angle $A$ , we will take the inverse of the trigonometric function of $\cos$ and find the value of the angle $A$
While the trigonometric functions give the ratio of any two sides of a right-angled triangle with a specific angle, the inverse trigonometric functions do the exact opposite and help us to calculate the value of that angle with respect to which a certain trigonometric ratio has been given in the question.
Therefore, we get,
$\Rightarrow \cos A=0.81$
$\Rightarrow A={{\cos }^{-1}}0.81$
The inverse of any trigonometric angle shows us only one angle, but there can be more angles with the same value.
The value of the above expression can be calculated using the log tables, where the value of the ${{\cos }^{-1}}=0.81$ will be given as $0.63rad\;$ or ${{35.9}^{\circ }}$ .
So, the value of the angle $A$ can be given as $0.63rad\;$ or ${{35.9}^{\circ }}$ depending on the mode of measuring the angles.
The conversion of an angle in the degree to radian can be given as ${{1}^{\circ }}=\dfrac{\pi }{{{180}^{\circ }}}$ .
Hence, the value of the angle $A$ is given by 0.63 rad or ${{35.9}^{\circ }}$

Note: Always remember that ${{\sin }^{-1}}$ is not the same as $\dfrac{1}{\sin }$ , most of the students get confused in this notation and get the idea that inverse trigonometric functions are just their fractional reciprocates. The same concept follows for all the remaining trigonometric functions as well, where reciprocating the function can give us a whole different trigonometric function and not the inverse of that trigonometric function.