What is the value of sin(arccos(-9/(sqrt(145)))) ?

The value of sin(arccos(-9/(sqrt(145)))) is (8sqrt(145))/(145)

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sin(arccos(-9/(sqrt(145))))

sin (arccos (- \frac{9}{145}))

\frac{8 145}{145}

Decimal Notation

0.66436 \dots

Solution steps

sin (arccos (- \frac{9}{145}))

Rewrite using trig identities:

sin (arccos (- \frac{9}{145})) = 1 - (- \frac{9}{145})^{2}

Use the following identity:

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

= 1 - (- \frac{9}{145})^{2}

= 1 - (- \frac{9}{145})^{2}

Simplify

= \frac{8 145}{145}

\frac{1}{cos ( 9 0 ^{\circ} )}

- e^{0} sin (2)

\frac{sin ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

- 2 sec (\frac{π}{4})

cot (29 0^{\circ})

What is the value of sin(arccos(-9/(sqrt(145)))) ?
The value of sin(arccos(-9/(sqrt(145)))) is (8sqrt(145))/(145)