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$\theta = 13^\circ \textrm{ , } 77^\circ$

Giancoli 6th Edition, Chapter 3, Problem 19



After getting the 25.08 by doing the math, how did you get 154.92?

I plugged in the numbers in my calculator and i got only 25.08 and i did not see where the 154.92 came from

Could you please tell me how that was done?

Thank you.

Hi ppadalkar,

154.92 is the other solutions to the trig. equation. For a positive Sine equation, the second solution is always 180 degrees minus the reference angle that your calculator gives you. In this case 154.92 = 180 - 25.08

This video seems pretty good for solving trig. equations, and I like the way it refers to the unit circle:

The bottom line: trig. equations always have at least two solutions (when dealing with right angled triangles, this second solution is extraneous since it's more than 90, and you never think about it, but when you're not working with triangles, like in this question, the second solution might be important).

You are saving my life. My physics teacher does not help me with these problems near as well as you explain it. Thank you so much

Thanks for the great feedback kelmerin2017, I'm really grateful that the solutions are helpful.

Good luck with your courses,
Mr. Dychko