Question

How do you find the value of \[\tan 90\]?

Answer 1

Hint:
The given problem is based on trigonometry. To solve the problem, we can apply trigonometric identities. Firstly, we need to know about the trigonometric function. So, for that we have some basic discussion on that. The values of trigonometric functions are also dependent on their angles. That way, we can find the solution to a given problem.

Complete Step by step Solution:
 To solve the given problem, we can use the identities of trigonometric functions.
Firstly, know about the trigonometric functions, let's discuss.
Trigonometric functions: In mathematics, trigonometric functions are real functions which are real functions which relate an angle of a right-angled triangle to ratio of two side lengths.
There are six trigonometric ratios: \[{\text{sine, cosine, tangent, cosecant, secant and cotangent}}\]. We can also call the functions as \[{\text{sin, cos, tan, cosec, sec and cot}}\] respectively.
We can apply the trigonometric identities to solve the problem.
Trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the length of the sides of a triangle.
The trigonometric functions are considered at various angles like \[{{\text{0}}^ \circ },3{{\text{0}}^ \circ },{45^ \circ },9{{\text{0}}^ \circ },12{{\text{0}}^ \circ }\]…. And so on.
As we are given \[\tan 9{{\text{0}}^ \circ }\], so we have to check the value of \[\tan 9{{\text{0}}^ \circ }\].
The identity of \[\tan x = \dfrac{{\sin x}}{{\cos x}}\]
Replacing \[x\] by \[9{{\text{0}}^ \circ }\] in the identity and it becomes:
\[\tan {90^ \circ } = \dfrac{{\sin {{90}^ \circ }}}{{\cos {{90}^ \circ }}}......................(A)\]
As the value of \[\cos 9{{\text{0}}^ \circ }\] is \[0\] and the value of \[\sin 9{{\text{0}}^ \circ }\] is \[1\].
Substituting in above equation (A), we get:
\[\tan {90^ \circ } = \dfrac{1}{0}\]
As the numerator is \[1\] and the denominator is \[0\]. So, the function is undefined. In other words, we cannot define the value of \[\tan {90^ \circ }\].

Note:
The given problem is based on trigonometric functions. Astronomers use trigonometry to calculate how far stars and planets are from the earth. Trigonometry can be used to make the roof of a house and height of roof in a building.