Question

Will you help me find the Exact value of sec pi/3 and help me under stand how to

Answer 1

To find the exact value of sec π/3, use a sp cial triangle with an angle

π/3 radians=60º.

Consider an equilateral triangle with each side length of 1 unit.

Recall that each angle in an equilateral triangle is 60º.

Draw the altitude of the triangle. Note that the altitude of an equilateral triangle is an angle bisector of the vertical angle and also a perpendicular bisector of its base:

Recall that the Secant Ratio in a right triangle is given as:

`\sec\theta=\frac{\text{ Hypotenuse}}{\text{ Adjacent}}`

Substitute θ=60º, hypotenuse=1, and adjacent=1/2 into the equation:

`\begin{gathered} \sec60^(\circ)=(1)/((1)/(2))=(2)/(1)=2 \\ \Rightarrow\sec60^(\circ)=2 \\ \Rightarrow\sec(\pi)/(3)=2 \end{gathered}`

The exact value of sec π/3 is 2.