What is sec(arctan(-4/3)+pin) ?

The solution to sec(arctan(-4/3)+pin) is 5/(3(-1)^n)

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simplify sec(arctan(-4/3)+pin)

simplify

sec (arctan (- \frac{4}{3}) + πn)

\frac{5}{3 ( - 1 ) ^{n}}

Solution steps

sec (arctan (- \frac{4}{3}) + πn)

Rewrite using trig identities

= \frac{1}{\frac{3}{5} cos ( πn ) + \frac{4}{5} sin ( πn )}

Use the basic trigonometric identity:

sin (nπ) = 0

= \frac{1}{cos ( nπ ) \frac{3}{5} + 0 \cdot \frac{4}{5}}

Use the basic trigonometric identity:

cos (nπ) = (- 1)^{n}

= \frac{1}{( - 1 ) ^{n} \frac{3}{5} + 0 \cdot \frac{4}{5}}

Simplify

= \frac{5}{3 ( - 1 ) ^{n}}

tan (θ + 90 0^{\circ})

sec (2) (a x + b) d x

cos (\frac{π}{4} + P)

3 sin (2 x - \frac{π}{6})

cos (- 4 r)

What is sec(arctan(-4/3)+pin) ?
The solution to sec(arctan(-4/3)+pin) is 5/(3(-1)^n)