What does it mean when they say Trigonometric Ratios of “Standard Angle”?

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First, let me be clear. I understand what is a "Standard Angle" or "Angle in Standard Position", my question is why are we interested in the Trig Ratios of only standard angles? How does non-standard angle affect the result?



PS : I'm a high schooler, starting out with Trig. Forgive me if this question sounds dumb. I just can't seem to accept why only "Standard Angles"?




trigonometry




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  • 1




    I don't know what a "Standard Angle" or "Angle in Standard Position" is, can you explain?
    – user2520938
    yesterday










  • I've never heard of such a term, but I'll guess. Right triangle, with base horizontal and opposite side on the right, vertical upwards. Angle in the lower left corner. You then have angles between $0^circ$ and $90^circ$.
    – herb steinberg
    yesterday







  • 1




    @user2520938 you can look it up on YouTube. Although I'll just tell you anyway. An angle whose initial arm lies along the positive direction of X axis and vertex at origin. Eg : youtu.be/ABDKOmamIwo
    – William
    yesterday










  • @herbsteinberg read my recent comment :)
    – William
    yesterday






  • 1




    Trig ratios are defined for all angles, but "standard angles" provide some instructional advantages. For instance, we can use descriptors like "First/Second/Third/Fourth-Quadrant Angles" depending upon where the terminal arm lies, instead of the unwieldy "acute angle", "obtuse angle", "angle between $180^circ$ and $270^circ$", "angle between $270^circ$ and $360^circ$". More-importantly, the cosine and sine values of a standard angle are exactly the $x$- and $y$- coordinates of the point where the terminal arm meets "the unit circle", which is helpful in learning how the signs work. Etc.
    – Blue
    yesterday














up vote
2
down vote

favorite












First, let me be clear. I understand what is a "Standard Angle" or "Angle in Standard Position", my question is why are we interested in the Trig Ratios of only standard angles? How does non-standard angle affect the result?



PS : I'm a high schooler, starting out with Trig. Forgive me if this question sounds dumb. I just can't seem to accept why only "Standard Angles"?




trigonometry




share|cite|improve this question

















  • 1




    I don't know what a "Standard Angle" or "Angle in Standard Position" is, can you explain?
    – user2520938
    yesterday










  • I've never heard of such a term, but I'll guess. Right triangle, with base horizontal and opposite side on the right, vertical upwards. Angle in the lower left corner. You then have angles between $0^circ$ and $90^circ$.
    – herb steinberg
    yesterday







  • 1




    @user2520938 you can look it up on YouTube. Although I'll just tell you anyway. An angle whose initial arm lies along the positive direction of X axis and vertex at origin. Eg : youtu.be/ABDKOmamIwo
    – William
    yesterday










  • @herbsteinberg read my recent comment :)
    – William
    yesterday






  • 1




    Trig ratios are defined for all angles, but "standard angles" provide some instructional advantages. For instance, we can use descriptors like "First/Second/Third/Fourth-Quadrant Angles" depending upon where the terminal arm lies, instead of the unwieldy "acute angle", "obtuse angle", "angle between $180^circ$ and $270^circ$", "angle between $270^circ$ and $360^circ$". More-importantly, the cosine and sine values of a standard angle are exactly the $x$- and $y$- coordinates of the point where the terminal arm meets "the unit circle", which is helpful in learning how the signs work. Etc.
    – Blue
    yesterday












up vote
2
down vote

favorite









up vote
2
down vote

favorite











First, let me be clear. I understand what is a "Standard Angle" or "Angle in Standard Position", my question is why are we interested in the Trig Ratios of only standard angles? How does non-standard angle affect the result?



PS : I'm a high schooler, starting out with Trig. Forgive me if this question sounds dumb. I just can't seem to accept why only "Standard Angles"?




trigonometry




share|cite|improve this question













First, let me be clear. I understand what is a "Standard Angle" or "Angle in Standard Position", my question is why are we interested in the Trig Ratios of only standard angles? How does non-standard angle affect the result?



PS : I'm a high schooler, starting out with Trig. Forgive me if this question sounds dumb. I just can't seem to accept why only "Standard Angles"?





trigonometry





share|cite|improve this question












share|cite|improve this question




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  • 1




    I don't know what a "Standard Angle" or "Angle in Standard Position" is, can you explain?
    – user2520938
    yesterday










  • I've never heard of such a term, but I'll guess. Right triangle, with base horizontal and opposite side on the right, vertical upwards. Angle in the lower left corner. You then have angles between $0^circ$ and $90^circ$.
    – herb steinberg
    yesterday







  • 1




    @user2520938 you can look it up on YouTube. Although I'll just tell you anyway. An angle whose initial arm lies along the positive direction of X axis and vertex at origin. Eg : youtu.be/ABDKOmamIwo
    – William
    yesterday










  • @herbsteinberg read my recent comment :)
    – William
    yesterday






  • 1




    Trig ratios are defined for all angles, but "standard angles" provide some instructional advantages. For instance, we can use descriptors like "First/Second/Third/Fourth-Quadrant Angles" depending upon where the terminal arm lies, instead of the unwieldy "acute angle", "obtuse angle", "angle between $180^circ$ and $270^circ$", "angle between $270^circ$ and $360^circ$". More-importantly, the cosine and sine values of a standard angle are exactly the $x$- and $y$- coordinates of the point where the terminal arm meets "the unit circle", which is helpful in learning how the signs work. Etc.
    – Blue
    yesterday












  • 1




    I don't know what a "Standard Angle" or "Angle in Standard Position" is, can you explain?
    – user2520938
    yesterday










  • I've never heard of such a term, but I'll guess. Right triangle, with base horizontal and opposite side on the right, vertical upwards. Angle in the lower left corner. You then have angles between $0^circ$ and $90^circ$.
    – herb steinberg
    yesterday







  • 1




    @user2520938 you can look it up on YouTube. Although I'll just tell you anyway. An angle whose initial arm lies along the positive direction of X axis and vertex at origin. Eg : youtu.be/ABDKOmamIwo
    – William
    yesterday










  • @herbsteinberg read my recent comment :)
    – William
    yesterday






  • 1




    Trig ratios are defined for all angles, but "standard angles" provide some instructional advantages. For instance, we can use descriptors like "First/Second/Third/Fourth-Quadrant Angles" depending upon where the terminal arm lies, instead of the unwieldy "acute angle", "obtuse angle", "angle between $180^circ$ and $270^circ$", "angle between $270^circ$ and $360^circ$". More-importantly, the cosine and sine values of a standard angle are exactly the $x$- and $y$- coordinates of the point where the terminal arm meets "the unit circle", which is helpful in learning how the signs work. Etc.
    – Blue
    yesterday







1




1




I don't know what a "Standard Angle" or "Angle in Standard Position" is, can you explain?
– user2520938
yesterday




I don't know what a "Standard Angle" or "Angle in Standard Position" is, can you explain?
– user2520938
yesterday












I've never heard of such a term, but I'll guess. Right triangle, with base horizontal and opposite side on the right, vertical upwards. Angle in the lower left corner. You then have angles between $0^circ$ and $90^circ$.
– herb steinberg
yesterday





I've never heard of such a term, but I'll guess. Right triangle, with base horizontal and opposite side on the right, vertical upwards. Angle in the lower left corner. You then have angles between $0^circ$ and $90^circ$.
– herb steinberg
yesterday





1




1




@user2520938 you can look it up on YouTube. Although I'll just tell you anyway. An angle whose initial arm lies along the positive direction of X axis and vertex at origin. Eg : youtu.be/ABDKOmamIwo
– William
yesterday




@user2520938 you can look it up on YouTube. Although I'll just tell you anyway. An angle whose initial arm lies along the positive direction of X axis and vertex at origin. Eg : youtu.be/ABDKOmamIwo
– William
yesterday












@herbsteinberg read my recent comment :)
– William
yesterday




@herbsteinberg read my recent comment :)
– William
yesterday




1




1




Trig ratios are defined for all angles, but "standard angles" provide some instructional advantages. For instance, we can use descriptors like "First/Second/Third/Fourth-Quadrant Angles" depending upon where the terminal arm lies, instead of the unwieldy "acute angle", "obtuse angle", "angle between $180^circ$ and $270^circ$", "angle between $270^circ$ and $360^circ$". More-importantly, the cosine and sine values of a standard angle are exactly the $x$- and $y$- coordinates of the point where the terminal arm meets "the unit circle", which is helpful in learning how the signs work. Etc.
– Blue
yesterday




Trig ratios are defined for all angles, but "standard angles" provide some instructional advantages. For instance, we can use descriptors like "First/Second/Third/Fourth-Quadrant Angles" depending upon where the terminal arm lies, instead of the unwieldy "acute angle", "obtuse angle", "angle between $180^circ$ and $270^circ$", "angle between $270^circ$ and $360^circ$". More-importantly, the cosine and sine values of a standard angle are exactly the $x$- and $y$- coordinates of the point where the terminal arm meets "the unit circle", which is helpful in learning how the signs work. Etc.
– Blue
yesterday















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