## Bbambino1976 2 years ago express sin 205degrees in terms of the sine of a positive acute angle. Do not evaluate.

1. Bbambino1976

an airplane propeler blade is 2.80ft, and rotates @ 2200 r/min. What is the linear velocity of a point on the tip of the blade?

2. Jbo11

have you learned about special trig rules with trig functions?

3. Bbambino1976

4. Bbambino1976

5. Jbo11

ok I'm sure now, for sin(205) to have it be an acute angle it has to be less than 90, and sin(25) works and is positive

6. Jbo11

Then your propeller one is difficult to explain, I found the same problem that is explained here on page 16 http://www.nunamaker.com/mathlady/Math%20181%20Chapter%2010%20Trig%20Functions%20Term%200306.pdf

7. Bbambino1976

Let me explain this and please tell me if I got it or not?

8. Bbambino1976

sin is positive in qued 1 or 2, so u subtract from 205 untill u get to 180? hence the 25.

9. Jbo11

um well not quite. So first info is given that the angle needs to be acute. And an acute angle must be less than 90 degrees, and this is taught in geometry. So by that definition, you know you are looking for an angle in the first quadrant. Second, it tells you need sin that is equivalent to sin(205) so hopefully with this picture it will help

10. Jbo11

|dw:1383427677574:dw|

11. Jbo11

so by using those rules 1. acute is less than 90 degrees 2. sin must be positive 3. the angle you are looking for has paired angle. you find the angle by 205-180 because you are looking for an angle that is exactly half around the unit circle which is 360 degrees

12. Bbambino1976

so the acute angles of A & B have the same degree measurement?

13. Jbo11

yup, only difference is one is negative and the other positive. if you have a calculator you can show yourself they are the same too. sin(205)=sin(25)

14. Bbambino1976

cool learning is fun! when i put sin(25) in my calculator i get 0.422.

15. Jbo11

haha sure is, and ye, the point of me telling you to try your calculator was to see that the decimal answer you get for sin(205) is the same as sin(25) just one is + and the other -

16. Jbo11

so sin (205) should be -0.422