What is the value of sec(arctan(3/2)) ?

The value of sec(arctan(3/2)) is (sqrt(13))/2

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sec(arctan(3/2))

sec (arctan (\frac{3}{2}))

\frac{13}{2}

Decimal Notation

1.80277 \dots

Solution steps

sec (arctan (\frac{3}{2}))

Rewrite using trig identities:

sec (arctan (\frac{3}{2})) = 1 + (\frac{3}{2})^{2}

Use the following identity:

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

= 1 + (\frac{3}{2})^{2}

= 1 + (\frac{3}{2})^{2}

Simplify

= \frac{13}{2}

13 + cos (\frac{π}{2})

tan (2 5^{\circ}) - \frac{cos ( 6 5 ^{\circ} )}{cos ( 2 5 ^{\circ} )}

3 sin (3 π)

\frac{tan ( 2 0 ^{\circ} )}{cot ( 7 0 ^{\circ} )}

sin (19. 5^{\circ})

What is the value of sec(arctan(3/2)) ?
The value of sec(arctan(3/2)) is (sqrt(13))/2