Use the figure below to answer the following questions 02040

Use the figure below to answer the following questions. 020406 08 12 IA 13 l 23 a. Approximate the measure of the indicated angle, n, measured in radians. radians Preview b. Using the figure above, and without using a calculator, approximate the value of 2 sin(n). Preview c. Using your answer from part (b), approximate the value ofsin(n). d using the figure above, and without using a calculator annnoximate the value of 2ooslnl 5201. ...pdf Doc120516-1205201....pdf

Solution

a. tan theta=y/x

the point is (-.4,-2)

tan theta=0.4/2

theta=tan^-1(.4/2)=78.7degree

and its in third quadrant.Therefore theta = 180+78.7=258.7 degree=258.7*pi/180 radian= 4.51 radian

b. 2sin n=2 sin 258.7= 2sin(180+78.7)

sin(180+theta)=-cos theta

2sin(180+78.7)=-2cos78.7

And cos theta=adjacent/hypotenuse

here adjacent=0.4    and opposite=2

Therefore hypotenuse=sqrt(4+.16)=sqrt4.16=2.04

cos x=0.4/2.04

-2 cos x= -0.4/1.02= -.2/.51

c. sin n=cos -78.7= -.4/2.04= -.1/.51

d. 2cos n= 2cos 258.7=2cos(180+78.7)=-2sin 78.7=-2*2/ 2.04=-1/ .51

e. cos n=-sin 78.7= - 2/2.04=-1/ 1.02