Solving $sin(-theta)=0.35 $. Is $sin$ postive or negative? Where are the angles located?











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My question:
$$sin(-theta)=0.35 qquadtext{range: } 0<theta<360$$



Is $sin$ positive or negative in this case? and where would the angles locate at?



Thank you!






algebra-precalculus trigonometry







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  • Your pre-edit $-20.5^circ$ and $-159.5^circ$ are not in the interval $[0^circ,360^circ)$. So you need to find the equivalent angles which are in that interval
    – Henry
    9 hours ago












  • @Henry is sin positive or negative?
    – Tfue
    9 hours ago










  • $sin$ gives positive values for angles between $0^circ$ and $180^circ$ and between $-360^circ$ and $-180^circ$ and between $360^circ$ and $540^circ$ and ..., while $sin$ gives negative values for angles between between $-180^circ$ and $0^circ$ and between $180^circ$ and $360^circ$ and .... In general you have $-1 le sin(theta) le 1$
    – Henry
    9 hours ago








  • 1




    @Tfue: The question “is sin positive or negative” is meaningless. The sine of what? The value $sin(-theta)$ is obvious positive, though, since it's equal to $0.35$ by definition.
    – Hans Lundmark
    8 hours ago















up vote
0
down vote

favorite












My question:
$$sin(-theta)=0.35 qquadtext{range: } 0<theta<360$$



Is $sin$ positive or negative in this case? and where would the angles locate at?



Thank you!






algebra-precalculus trigonometry







share|cite|improve this question
























  • Your pre-edit $-20.5^circ$ and $-159.5^circ$ are not in the interval $[0^circ,360^circ)$. So you need to find the equivalent angles which are in that interval
    – Henry
    9 hours ago












  • @Henry is sin positive or negative?
    – Tfue
    9 hours ago










  • $sin$ gives positive values for angles between $0^circ$ and $180^circ$ and between $-360^circ$ and $-180^circ$ and between $360^circ$ and $540^circ$ and ..., while $sin$ gives negative values for angles between between $-180^circ$ and $0^circ$ and between $180^circ$ and $360^circ$ and .... In general you have $-1 le sin(theta) le 1$
    – Henry
    9 hours ago








  • 1




    @Tfue: The question “is sin positive or negative” is meaningless. The sine of what? The value $sin(-theta)$ is obvious positive, though, since it's equal to $0.35$ by definition.
    – Hans Lundmark
    8 hours ago













up vote
0
down vote

favorite









up vote
0
down vote

favorite











My question:
$$sin(-theta)=0.35 qquadtext{range: } 0<theta<360$$



Is $sin$ positive or negative in this case? and where would the angles locate at?



Thank you!






algebra-precalculus trigonometry







share|cite|improve this question















My question:
$$sin(-theta)=0.35 qquadtext{range: } 0<theta<360$$



Is $sin$ positive or negative in this case? and where would the angles locate at?



Thank you!






algebra-precalculus trigonometry




algebra-precalculus trigonometry






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 9 hours ago









Blue

46.1k869145




46.1k869145










asked 9 hours ago









Tfue

416




416












  • Your pre-edit $-20.5^circ$ and $-159.5^circ$ are not in the interval $[0^circ,360^circ)$. So you need to find the equivalent angles which are in that interval
    – Henry
    9 hours ago












  • @Henry is sin positive or negative?
    – Tfue
    9 hours ago










  • $sin$ gives positive values for angles between $0^circ$ and $180^circ$ and between $-360^circ$ and $-180^circ$ and between $360^circ$ and $540^circ$ and ..., while $sin$ gives negative values for angles between between $-180^circ$ and $0^circ$ and between $180^circ$ and $360^circ$ and .... In general you have $-1 le sin(theta) le 1$
    – Henry
    9 hours ago








  • 1




    @Tfue: The question “is sin positive or negative” is meaningless. The sine of what? The value $sin(-theta)$ is obvious positive, though, since it's equal to $0.35$ by definition.
    – Hans Lundmark
    8 hours ago


















  • Your pre-edit $-20.5^circ$ and $-159.5^circ$ are not in the interval $[0^circ,360^circ)$. So you need to find the equivalent angles which are in that interval
    – Henry
    9 hours ago












  • @Henry is sin positive or negative?
    – Tfue
    9 hours ago










  • $sin$ gives positive values for angles between $0^circ$ and $180^circ$ and between $-360^circ$ and $-180^circ$ and between $360^circ$ and $540^circ$ and ..., while $sin$ gives negative values for angles between between $-180^circ$ and $0^circ$ and between $180^circ$ and $360^circ$ and .... In general you have $-1 le sin(theta) le 1$
    – Henry
    9 hours ago








  • 1




    @Tfue: The question “is sin positive or negative” is meaningless. The sine of what? The value $sin(-theta)$ is obvious positive, though, since it's equal to $0.35$ by definition.
    – Hans Lundmark
    8 hours ago
















Your pre-edit $-20.5^circ$ and $-159.5^circ$ are not in the interval $[0^circ,360^circ)$. So you need to find the equivalent angles which are in that interval
– Henry
9 hours ago






Your pre-edit $-20.5^circ$ and $-159.5^circ$ are not in the interval $[0^circ,360^circ)$. So you need to find the equivalent angles which are in that interval
– Henry
9 hours ago














@Henry is sin positive or negative?
– Tfue
9 hours ago




@Henry is sin positive or negative?
– Tfue
9 hours ago












$sin$ gives positive values for angles between $0^circ$ and $180^circ$ and between $-360^circ$ and $-180^circ$ and between $360^circ$ and $540^circ$ and ..., while $sin$ gives negative values for angles between between $-180^circ$ and $0^circ$ and between $180^circ$ and $360^circ$ and .... In general you have $-1 le sin(theta) le 1$
– Henry
9 hours ago






$sin$ gives positive values for angles between $0^circ$ and $180^circ$ and between $-360^circ$ and $-180^circ$ and between $360^circ$ and $540^circ$ and ..., while $sin$ gives negative values for angles between between $-180^circ$ and $0^circ$ and between $180^circ$ and $360^circ$ and .... In general you have $-1 le sin(theta) le 1$
– Henry
9 hours ago






1




1




@Tfue: The question “is sin positive or negative” is meaningless. The sine of what? The value $sin(-theta)$ is obvious positive, though, since it's equal to $0.35$ by definition.
– Hans Lundmark
8 hours ago




@Tfue: The question “is sin positive or negative” is meaningless. The sine of what? The value $sin(-theta)$ is obvious positive, though, since it's equal to $0.35$ by definition.
– Hans Lundmark
8 hours ago










1 Answer
1






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In these type of question, we should draw the graph of $sin x$, and do some algebraic manipulation based on that. We know that $$sin(-theta) = -sin(theta)$$ therefore we are trying to find the solution of $sin x = -0.35,$ where $x in (0^{circ},360^{circ})$.



From the graph, we see that, $sin(x)$ is negative in $x in(180^{circ},360^{circ})$, hence we will have two solutions one in each of the intervals $(180^{circ},270^{circ})$ and $(270^{circ},360^{circ})$ (as it takes all values between $0$ and $-1$ in both of these intervals).



If you want better bounds on where the roots will lie, you should consider the increasing-decreasing nature of the graph and decimal values of the known values of sin function (For example, $sin(x)$ takes values between $0$ and $-0.707$ for $x in (180^{circ},225^{circ}),$ so $-0.35$ will occur in this interval between $180^{circ}$ and $270^{circ},$ which is a better bound).



Hope it helps:)






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    In these type of question, we should draw the graph of $sin x$, and do some algebraic manipulation based on that. We know that $$sin(-theta) = -sin(theta)$$ therefore we are trying to find the solution of $sin x = -0.35,$ where $x in (0^{circ},360^{circ})$.



    From the graph, we see that, $sin(x)$ is negative in $x in(180^{circ},360^{circ})$, hence we will have two solutions one in each of the intervals $(180^{circ},270^{circ})$ and $(270^{circ},360^{circ})$ (as it takes all values between $0$ and $-1$ in both of these intervals).



    If you want better bounds on where the roots will lie, you should consider the increasing-decreasing nature of the graph and decimal values of the known values of sin function (For example, $sin(x)$ takes values between $0$ and $-0.707$ for $x in (180^{circ},225^{circ}),$ so $-0.35$ will occur in this interval between $180^{circ}$ and $270^{circ},$ which is a better bound).



    Hope it helps:)






    share|cite|improve this answer



























      up vote
      0
      down vote



      accepted










      In these type of question, we should draw the graph of $sin x$, and do some algebraic manipulation based on that. We know that $$sin(-theta) = -sin(theta)$$ therefore we are trying to find the solution of $sin x = -0.35,$ where $x in (0^{circ},360^{circ})$.



      From the graph, we see that, $sin(x)$ is negative in $x in(180^{circ},360^{circ})$, hence we will have two solutions one in each of the intervals $(180^{circ},270^{circ})$ and $(270^{circ},360^{circ})$ (as it takes all values between $0$ and $-1$ in both of these intervals).



      If you want better bounds on where the roots will lie, you should consider the increasing-decreasing nature of the graph and decimal values of the known values of sin function (For example, $sin(x)$ takes values between $0$ and $-0.707$ for $x in (180^{circ},225^{circ}),$ so $-0.35$ will occur in this interval between $180^{circ}$ and $270^{circ},$ which is a better bound).



      Hope it helps:)






      share|cite|improve this answer

























        up vote
        0
        down vote



        accepted







        up vote
        0
        down vote



        accepted






        In these type of question, we should draw the graph of $sin x$, and do some algebraic manipulation based on that. We know that $$sin(-theta) = -sin(theta)$$ therefore we are trying to find the solution of $sin x = -0.35,$ where $x in (0^{circ},360^{circ})$.



        From the graph, we see that, $sin(x)$ is negative in $x in(180^{circ},360^{circ})$, hence we will have two solutions one in each of the intervals $(180^{circ},270^{circ})$ and $(270^{circ},360^{circ})$ (as it takes all values between $0$ and $-1$ in both of these intervals).



        If you want better bounds on where the roots will lie, you should consider the increasing-decreasing nature of the graph and decimal values of the known values of sin function (For example, $sin(x)$ takes values between $0$ and $-0.707$ for $x in (180^{circ},225^{circ}),$ so $-0.35$ will occur in this interval between $180^{circ}$ and $270^{circ},$ which is a better bound).



        Hope it helps:)






        share|cite|improve this answer














        In these type of question, we should draw the graph of $sin x$, and do some algebraic manipulation based on that. We know that $$sin(-theta) = -sin(theta)$$ therefore we are trying to find the solution of $sin x = -0.35,$ where $x in (0^{circ},360^{circ})$.



        From the graph, we see that, $sin(x)$ is negative in $x in(180^{circ},360^{circ})$, hence we will have two solutions one in each of the intervals $(180^{circ},270^{circ})$ and $(270^{circ},360^{circ})$ (as it takes all values between $0$ and $-1$ in both of these intervals).



        If you want better bounds on where the roots will lie, you should consider the increasing-decreasing nature of the graph and decimal values of the known values of sin function (For example, $sin(x)$ takes values between $0$ and $-0.707$ for $x in (180^{circ},225^{circ}),$ so $-0.35$ will occur in this interval between $180^{circ}$ and $270^{circ},$ which is a better bound).



        Hope it helps:)







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited 7 hours ago









        user376343

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        answered 9 hours ago









        Crazy for maths

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