Solve the Multiple-Angle Equation in the Interval $[ 0,2 \pi )$

question 57

Multiple Choice

Solve the multiple-angle equation in the interval $[ 0,2 \pi )$ .
$\tan 2 x = - 1$

• A) \(x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }\)
• B) \(x = \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }\)
• C) \(x = \frac { 3 \pi } { 8 } , \frac { 7 \pi } { 8 } , \frac { 11 \pi } { 8 } , \frac { 15 \pi } { 8 }\)
• D) \(x = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }\)
• E) \(x = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }\).

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Definitions:

Project's Payback

A calculation that determines the duration required for an investment to generate cash flows or profits enough to recover the initial investment cost.

WACC

Weighted Average Cost of Capital; the average rate of return a company must pay its security holders to finance its assets.

MIRR

The Modified Internal Rate of Return, a financial metric that measures the profitability of an investment while considering the cost of borrowing and reinvestment of cash flows.

Projected MIRR

Projected MIRR refers to the estimated modified internal rate of return, a comprehensive measure of an investment’s attractiveness, adjusting for the cost of capital and cash flow reinvestment rates.