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

The value of sec(arcsin(2/3)) is (3sqrt(5))/5

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sec(arcsin(2/3))

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

\frac{3 5}{5}

Decimal Notation

1.34164 \dots

Solution steps

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

Rewrite using trig identities:

sec (arcsin (\frac{2}{3})) = \frac{1 - ( \frac{2}{3} ) ^{2}}{1 - ( \frac{2}{3} ) ^{2}}

Use the following identity:

sec (arcsin (x)) = \frac{1 - x ^{2}}{1 - x ^{2}}

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

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

Simplify

= \frac{3 5}{5}

5 cos (2 0^{\circ})

- cot (\frac{3 π}{4}) csc (\frac{3 π}{4})

1 - cos (\frac{3 π}{2})

sec (- 60 0^{\circ})

50 \cdot cos (3 7^{\circ})

What is the value of sec(arcsin(2/3)) ?
The value of sec(arcsin(2/3)) is (3sqrt(5))/5