trig problem

[icat]

the problem is sin(theta)=-0.7 for (theta)<=0<=360

i used arcsin(-0.7)=-44.4+360=315.6, which isone of the answers.

for the second answer, i added 270 to get 225.6, which is not the right answer, it is supposed to be 224.4. does anyone know what I am doing wrong, and could somone please explain to me how to solve this problem?

 

[tkhunny]

Why did you add 270º? The sine function is symmetric about 270º. It should be the same distance away on both sides.

315.6 - 270.0 = 45.6
270.0 - 45.6 = 224.4

You must think about the nature of the problem. The use of some formula for which you may or may not remember all the rules simply isn't very effective.

 

[galactus]

Sine has a period of 180 degrees.

Add 180 to -44.427. Subtract that from 360.

arcsin(.7)=44.427. Add 180 to that.

sin(-44.427)=-.7      sin(44.427)=.7
sin(135.573)=.7       sin(224.427)=-.7
sin(315.573)=-.7      sin(404.427)=.7
sin(495.573)=.7       sin(584.427)=-.7
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See the pattern?.