Question

What is the exact value of \[\sec ( - {330^ \circ })\]?

Answer 1

Hint: At first, we will find the given function even or odd.
According to that, we will apply the formula. Next, we will try to find the quadrant of the given function and finally we can find the value of the given function.

Complete step-by-step solution:
It is given that; \[\sec ( - {330^ \circ })\]
We have to find the exact value of \[\sec ( - {330^ \circ })\].
Since \[\sec ( - {330^ \circ })\] is an even function. So, we have \[\sec ( - {330^ \circ }) = \sec ({330^ \circ })\]
Now, we have \[{330^ \circ } = {360^ \circ } - {30^ \circ }\] which means it lies on the first quadrant.
We know that the value of \[\sec {30^ \circ }\]is positive.
Again,
\[\sec {30^ \circ } = \dfrac{1}{{\cos {{30}^ \circ }}}\]
Substitute the value of \[\cos {30^ \circ } = \dfrac{{\sqrt 3 }}{2}\] we get,
\[\sec {30^ \circ } = \dfrac{2}{{\sqrt 3 }}\]
Hence, the value of \[\sec ( - {330^ \circ })\]is \[\dfrac{2}{{\sqrt 3 }}\].

Note: A function is even if \[f( - x) = f(x)\] for all \[x\].
This means that the function is the same for (+ve x-axis, +ve y-axis) and (-ve x-axis,-ve y-axis), or graphically, symmetric about the y-axis.
A quadrant is one of the four sections on a Cartesian plane. Each quadrant includes a combination of positive and negative values for x and y.
There are four graph quadrants that make up the Cartesian plane. Each graph quadrant has a distinct combination of positive and negative values.
Here are the graph quadrants and their values:
Quadrant I: The first quadrant is in the upper right-hand corner of the plane. Both x and y have positive values in this quadrant.
Quadrant II: The second quadrant is in the upper left-hand corner of the plane. X has negative values in this quadrant and y has positive values.
Quadrant III: The third quadrant is in the bottom left corner. Both x and y have negative values in this quadrant.
Quadrant IV: The fourth quadrant is in the bottom right corner. X has positive values in this quadrant and y has negative values.