Question

How do you evaluate the expression sec30?

Answer 1

Hint: To solve the given question, we should know the relationship between the trigonometry ratio cosine and secant, using their relationship or conversion formula we will solve the given problem. These two ratios are inverse of each other, algebraically we can express it as \[\sec x=\dfrac{1}{\cos x}\]. Here, x is any angle in radian or degrees. As cosine can also be zero for some values of x, we should be careful around such points while evaluating secant values.

Complete step by step answer:
We are asked to find the value of sec30. To solve this question, we will use the conversion formula between the cosine ratio and secant ratio.
We know that the two ratios are related as \[\sec x=\dfrac{1}{\cos x}\]. Here, x is any angle in radian and degrees. We are asked to find the value of sec30, so for this question the value of x is 30. Substituting the value of x, we get
\[\sec {{30}^{\circ }}=\dfrac{1}{\cos {{30}^{\circ }}}\]
We know the value of cos30 is \[\dfrac{\sqrt{3}}{2}\]. substituting this in the above equation, we get
\[\sec {{30}^{\circ }}=\dfrac{1}{\dfrac{\sqrt{3}}{2}}\]
Simplifying the above equation, we get
\[\sec {{30}^{\circ }}=\dfrac{2}{\sqrt{3}}\]
Thus, we get the value of sec30.

Note: To solve such a problem, we should know the values of different trigonometric ratios at standard values of angles. By using the values of sine, cosine we can find the value of any other trigonometric ratio at the angle. Calculation mistakes should be avoided. As 30 is a special angle, we can also remember the value of sec30 and use it directly in solving questions.