What is the value of cos(arcsin(1/2)) ?

The value of cos(arcsin(1/2)) is (sqrt(3))/2

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cos(arcsin(1/2))

cos (arcsin (\frac{1}{2}))

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

cos (arcsin (\frac{1}{2}))

Rewrite using trig identities:

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

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

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

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

Simplify

= \frac{3}{2}

tan (67. 5^{\circ})

tan^{2} (x) = \frac{1}{3}

4 sin^{2} (x) - 1 = 0

sin (21 0^{\circ})

cos (- \frac{π}{12})

What is the value of cos(arcsin(1/2)) ?
The value of cos(arcsin(1/2)) is (sqrt(3))/2