What is the value of sec(arctan(-4)) ?

The value of sec(arctan(-4)) is square root of 17

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sec(arctan(-4))

sec (arctan (- 4))

17

Decimal Notation

4.12310 \dots

Solution steps

sec (arctan (- 4))

Rewrite using trig identities:

sec (arctan (- 4)) = 1 + (- 4)^{2}

Use the following identity:

sec (arctan (x)) = 1 + x^{2}

= 1 + (- 4)^{2}

= 1 + (- 4)^{2}

Simplify

= 17

\frac{cos ( 3 0 ^{\circ} ) + tan ( 6 0 ^{\circ} )}{2 - cos ^{2} ( 4 5 ^{\circ} )}

sin (\frac{arctan ( \frac{4}{3} )}{2})

cos (30 5^{\circ})

2 cos^{2} (0.19) - 1

tan (5.9)

What is the value of sec(arctan(-4)) ?
The value of sec(arctan(-4)) is square root of 17