Find the Exact Value arccsc(sec((2pi)/3))

$arccsc (\sec (\frac{2 π}{3}))$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because secant is negative in the second quadrant.

$arccsc (- \sec (\frac{π}{3}))$

Step 2

The exact value of $\sec (\frac{π}{3})$ is $2$ .

$arccsc (- 1 \cdot 2)$

Step 3

Multiply $- 1$ by $2$ .

$arccsc (- 2)$

Step 4

The exact value of $arccsc (- 2)$ is $- \frac{π}{6}$ .

$- \frac{π}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{6}$

Decimal Form:

$- 0.52359877 \dots$

Find the Exact Value arccsc(sec((2pi)/3))

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