What is the value of sin(arccos(-2/7)) ?

The value of sin(arccos(-2/7)) is (3sqrt(5))/7

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sin(arccos(-2/7))

sin (arccos (- \frac{2}{7}))

\frac{3 5}{7}

Decimal Notation

0.95831 \dots

Solution steps

sin (arccos (- \frac{2}{7}))

Rewrite using trig identities:

sin (arccos (- \frac{2}{7})) = 1 - (- \frac{2}{7})^{2}

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - (- \frac{2}{7})^{2}

= 1 - (- \frac{2}{7})^{2}

Simplify

= \frac{3 5}{7}

cos (1.5708)

arctan (\frac{- 5}{- 5})

sin (30 0^{\circ}) + cos (39 0^{\circ}) + tan (54 0^{\circ})

arctan (0.87)

cot^{2} (\frac{3 π}{4})

What is the value of sin(arccos(-2/7)) ?
The value of sin(arccos(-2/7)) is (3sqrt(5))/7