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
edited 9 hours ago
Blue
46.1k869145
asked 9 hours ago
Tfue
416
add a comment |
up vote
0
down vote
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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
edited 9 hours ago
Blue
46.1k869145
asked 9 hours ago
Tfue
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
add a comment |
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
edited 9 hours ago
Blue
46.1k869145
asked 9 hours ago
Tfue
416
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
edited 9 hours ago
Blue
46.1k869145
asked 9 hours ago
Tfue
416
edited 9 hours ago
Blue
46.1k869145
asked 9 hours ago
Tfue
416
edited 9 hours ago
Blue
46.1k869145
edited 9 hours ago
Blue
46.1k869145
edited 9 hours ago
Blue
46.1k869145
46.1k869145
asked 9 hours ago
Tfue
416
asked 9 hours ago
Tfue
416
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
add a comment |
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
add a comment |
1 Answer
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oldest
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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:)
edited 7 hours ago
user376343
2,0991715
answered 9 hours ago
Crazy for maths
3205
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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:)
edited 7 hours ago
user376343
2,0991715
answered 9 hours ago
Crazy for maths
3205
add a comment |
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:)
edited 7 hours ago
user376343
2,0991715
answered 9 hours ago
Crazy for maths
3205
add a comment |
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:)
edited 7 hours ago
user376343
2,0991715
answered 9 hours ago
Crazy for maths
3205
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:)
edited 7 hours ago
user376343
2,0991715
answered 9 hours ago
Crazy for maths
3205
edited 7 hours ago
user376343
2,0991715
edited 7 hours ago
user376343
2,0991715
edited 7 hours ago
user376343
2,0991715
2,0991715
answered 9 hours ago
Crazy for maths
3205
answered 9 hours ago
Crazy for maths
3205
answered 9 hours ago
Crazy for maths
3205
3205
add a comment |
add a comment |
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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