Question

A circle has a radius of 4 meters centered at the origin. Determine the measure of the angle (in radians) swept out counter-clockwise from the 3 o'clock position (the ray that connects (0,0) and (4,0)) and the indicated point.(3.51,1.918) metersθ= radians   (−0.737,0.675) radiiθ=  radians   (−3.392,−2.119) metersθ= radians   (0.96,−0.279)radiiθ=  radians

Answer 1

Input data

r = radius

r = 4m

angle from 3 o'clock

Procedure

a. (3.51, 1,918)

`\begin{gathered} \sin \theta=(1.918)/(4) \\ \theta=\sin ^(-1)((1.978)/(4))=0.517 \end{gathered}`

c. (-3.392, -2.119)

`\begin{gathered} \sin \theta=(-2.119)/(4) \\ \theta=\sin ^(-1)(-(2.119)/(4))=0.5583 \\ \theta=\pi+0.5583 \\ \theta=3.7\text{ rad} \end{gathered}`

b. (−0.737,0.675) radii

Translate into meters (-2.948, 2.7)

`\begin{gathered} \sin \theta=(2.7)/(4) \\ \theta=\sin ^(-1)((2.7)/(4)) \\ \theta=0.741 \\ \theta=\pi-0.741 \\ \theta=2.4 \end{gathered}`

d. (0.96,−0.279) radii

Translate into meters (3.84, -1.116)

`\begin{gathered} \sin \theta=(-1.116)/(4) \\ \theta=\sin ^(-1)((-1.116)/(4)) \\ \theta=0.282 \\ \theta=2\pi-0.282 \\ \theta=6\text{ rads} \end{gathered}`

Summary

a. 0.517 rad

b. 2.4 rad

c. 3.7 rad

d. 6 rad