Problem 86 - Algebra and Trigonometry Real Mathematics, Real People

Question

Determine whether the statement is true or false. Justify your answer. $$\sec 30^{\circ}=\csc 60^{\circ}$$

Step-by-Step Solution

Answer

The statement is false

Step 1: Find the value of sec 30°

Secant of an angle in a right triangle is the hypotenuse over the adjacent side. For a 30° angle in a right triangle, the secant is \(\frac{2\sqrt{3}}{2} = \sqrt{3}\)

Step 2: Find the value of csc 60°

Cosecant of an angle in a right triangle is the hypotenuse over the opposite side. For a 60°, the cosecant is \(\frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}\)

Step 3: Compare the value of sec 30° and csc 60°

We can see that \(\sqrt{3}\) is not equal to \(\frac{2\sqrt{3}}{3}\). So the statement is false.