How do you find the value for $sin (arccos (- \frac{1}{3}))$ $sin(arccos(-1/3))$ ?

Question

How do you find the value for $sin (arccos (- \frac{1}{3}))$ $sin(arccos(-1/3))$ ?

2 Answers

Impact of this question

2391 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-11T13:32:08

Use calculator to evaluate $θ = arccos (- \frac{1}{3})$ $theta = arccos(-1/3)$ , allow for $θ + π$ $theta+pi$ (since $cos (θ) = cos (θ + π)$ $cos(theta) = cos(theta+pi)$ ); use calculator to evaluate the two values of theta (within the $0$ $0$ to $2 π$ $2pi$ range.

Explanation:

Using caluclator
$XXXX$ $color(white)("XXXX")$ $arccos (- \frac{1}{3}) = 1.910633$ $arccos(-1/3) = 1.910633$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ i.e $cos (1.910633) = - \frac{1}{3}$ $cos(1.910633) = -1/3$
$XXXX$ $color(white)("XXXX")$ note that
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $cos (1.910633 + π)$ $cos(1.910633+pi)$ also $= - \frac{1}{3}$ $= -1/3$

Using calculator evaluate:
$XXXX$ $color(white)("XXXX")$ $sin (1.910633) = 0.942809$ $sin(1.910633) = 0.942809$
and
$XXXX$ $color(white)("XXXX")$ $sin (1.910633 + π) = sin (4.372552) = - 0.942809$ $sin(1.910633+pi) = sin(4.372552) = -0.942809$

Answer 2 · 2015-06-11T15:48:22

Find $sin (arccos (- \frac{1}{3}))$ $sin (arccos (-1/3))$

Explanation:

$cos x = - \frac{1}{3}$ $cos x = -1/3$ --> arc x?

Calculator gives $x = \pm 109.47$ $x = +- 109.47$ .
Now, find $sin (\pm 109.47)$ $sin (+- 109.47)$

sin (109.47) = 0.94
sin (-109.47) = -0.94

Science

Math

Humanities

... and beyond

How do you find the value for $sin (arccos (- \frac{1}{3}))$ $sin(arccos(-1/3))$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the value for sin(arccos(−13))sin(arccos(-1/3))?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you find the value for $sin (arccos (- \frac{1}{3}))$ $sin(arccos(-1/3))$ ?