Is SOH CAH TOA inherently in degrees or radians?
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up vote
0
down vote
favorite
Lets say for example I have a triangle like the one below:
If I find x by doing
$sin^-1dfrac 35$
is the resulting number in degrees or radians? I understand that a calculator can be set to return degrees or radians, but what is this number inherently? If I have misunderstood something then please let me know.
trigonometry
edited Aug 27 at 17:15
bjcolby15
8511816
asked Aug 27 at 17:08
Tyler S. Loeper
1064
add a comment |Â
up vote
0
down vote
favorite
Lets say for example I have a triangle like the one below:
If I find x by doing
$sin^-1dfrac 35$
is the resulting number in degrees or radians? I understand that a calculator can be set to return degrees or radians, but what is this number inherently? If I have misunderstood something then please let me know.
trigonometry
edited Aug 27 at 17:15
bjcolby15
8511816
asked Aug 27 at 17:08
Tyler S. Loeper
1064
Mostly radians, sometimes degrees.
– Love Invariants
Aug 27 at 17:09
1
The result of your calculation is going to depend on whether your calculator is in degrees or radians. SOH CAH TOA, though, is independent of radians or degrees, because it is going the other way.
– Adrian Keister
Aug 27 at 17:09
4
Sine of an angle is opposite length over hypotenuse, regardless of what units the angle is in. But you will need to decide what units you want to use to compute $sin^-1(3/5)$
– ziggurism
Aug 27 at 17:10
3
The resulting number is an angle. Angles do not inherently by themselves have a preferred unit of measurement, just like how length does not have a preference for meters versus feet. How you interpret that angle depends on what you want. If you want the result to be in radians then you have an answer of about $0.643$ (rad). If you want the result to be in degrees then you have an answer of about $36.87^circ$
– JMoravitz
Aug 27 at 17:11
It is generally preferred in the mathematical community to use radians as it makes several calculations "nicer." For example, in calculus if we interpret $sin(x)$ and $cos(x)$ as taking inputs in terms of amounts of radians we have the derivative of $sin$ being $fracddx[sin(x)]=cos(x)$. However, if we want to instead interpret inputs as degrees we would instead have $fracddx[sin(x)]=fracpi180cos(x)$. See this question.
– JMoravitz
Aug 27 at 17:17
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Lets say for example I have a triangle like the one below:
If I find x by doing
$sin^-1dfrac 35$
is the resulting number in degrees or radians? I understand that a calculator can be set to return degrees or radians, but what is this number inherently? If I have misunderstood something then please let me know.
trigonometry
edited Aug 27 at 17:15
bjcolby15
8511816
asked Aug 27 at 17:08
Tyler S. Loeper
1064
Lets say for example I have a triangle like the one below:
If I find x by doing
$sin^-1dfrac 35$
is the resulting number in degrees or radians? I understand that a calculator can be set to return degrees or radians, but what is this number inherently? If I have misunderstood something then please let me know.
trigonometry
edited Aug 27 at 17:15
bjcolby15
8511816
asked Aug 27 at 17:08
Tyler S. Loeper
1064
edited Aug 27 at 17:15
bjcolby15
8511816
edited Aug 27 at 17:15
bjcolby15
8511816
edited Aug 27 at 17:15
bjcolby15
8511816
8511816
asked Aug 27 at 17:08
Tyler S. Loeper
1064
asked Aug 27 at 17:08
Tyler S. Loeper
1064
asked Aug 27 at 17:08
Tyler S. Loeper
1064
1064
Mostly radians, sometimes degrees.
– Love Invariants
Aug 27 at 17:09
1
The result of your calculation is going to depend on whether your calculator is in degrees or radians. SOH CAH TOA, though, is independent of radians or degrees, because it is going the other way.
– Adrian Keister
Aug 27 at 17:09
4
Sine of an angle is opposite length over hypotenuse, regardless of what units the angle is in. But you will need to decide what units you want to use to compute $sin^-1(3/5)$
– ziggurism
Aug 27 at 17:10
3
The resulting number is an angle. Angles do not inherently by themselves have a preferred unit of measurement, just like how length does not have a preference for meters versus feet. How you interpret that angle depends on what you want. If you want the result to be in radians then you have an answer of about $0.643$ (rad). If you want the result to be in degrees then you have an answer of about $36.87^circ$
– JMoravitz
Aug 27 at 17:11
It is generally preferred in the mathematical community to use radians as it makes several calculations "nicer." For example, in calculus if we interpret $sin(x)$ and $cos(x)$ as taking inputs in terms of amounts of radians we have the derivative of $sin$ being $fracddx[sin(x)]=cos(x)$. However, if we want to instead interpret inputs as degrees we would instead have $fracddx[sin(x)]=fracpi180cos(x)$. See this question.
– JMoravitz
Aug 27 at 17:17
add a comment |Â
Mostly radians, sometimes degrees.
– Love Invariants
Aug 27 at 17:09
1
The result of your calculation is going to depend on whether your calculator is in degrees or radians. SOH CAH TOA, though, is independent of radians or degrees, because it is going the other way.
– Adrian Keister
Aug 27 at 17:09
4
Sine of an angle is opposite length over hypotenuse, regardless of what units the angle is in. But you will need to decide what units you want to use to compute $sin^-1(3/5)$
– ziggurism
Aug 27 at 17:10
3
The resulting number is an angle. Angles do not inherently by themselves have a preferred unit of measurement, just like how length does not have a preference for meters versus feet. How you interpret that angle depends on what you want. If you want the result to be in radians then you have an answer of about $0.643$ (rad). If you want the result to be in degrees then you have an answer of about $36.87^circ$
– JMoravitz
Aug 27 at 17:11
It is generally preferred in the mathematical community to use radians as it makes several calculations "nicer." For example, in calculus if we interpret $sin(x)$ and $cos(x)$ as taking inputs in terms of amounts of radians we have the derivative of $sin$ being $fracddx[sin(x)]=cos(x)$. However, if we want to instead interpret inputs as degrees we would instead have $fracddx[sin(x)]=fracpi180cos(x)$. See this question.
– JMoravitz
Aug 27 at 17:17
Mostly radians, sometimes degrees.
– Love Invariants
Aug 27 at 17:09
Mostly radians, sometimes degrees.
– Love Invariants
Aug 27 at 17:09
1
1
The result of your calculation is going to depend on whether your calculator is in degrees or radians. SOH CAH TOA, though, is independent of radians or degrees, because it is going the other way.
– Adrian Keister
Aug 27 at 17:09
The result of your calculation is going to depend on whether your calculator is in degrees or radians. SOH CAH TOA, though, is independent of radians or degrees, because it is going the other way.
– Adrian Keister
Aug 27 at 17:09
4
4
Sine of an angle is opposite length over hypotenuse, regardless of what units the angle is in. But you will need to decide what units you want to use to compute $sin^-1(3/5)$
– ziggurism
Aug 27 at 17:10
Sine of an angle is opposite length over hypotenuse, regardless of what units the angle is in. But you will need to decide what units you want to use to compute $sin^-1(3/5)$
– ziggurism
Aug 27 at 17:10
3
3
The resulting number is an angle. Angles do not inherently by themselves have a preferred unit of measurement, just like how length does not have a preference for meters versus feet. How you interpret that angle depends on what you want. If you want the result to be in radians then you have an answer of about $0.643$ (rad). If you want the result to be in degrees then you have an answer of about $36.87^circ$
– JMoravitz
Aug 27 at 17:11
The resulting number is an angle. Angles do not inherently by themselves have a preferred unit of measurement, just like how length does not have a preference for meters versus feet. How you interpret that angle depends on what you want. If you want the result to be in radians then you have an answer of about $0.643$ (rad). If you want the result to be in degrees then you have an answer of about $36.87^circ$
– JMoravitz
Aug 27 at 17:11
It is generally preferred in the mathematical community to use radians as it makes several calculations "nicer." For example, in calculus if we interpret $sin(x)$ and $cos(x)$ as taking inputs in terms of amounts of radians we have the derivative of $sin$ being $fracddx[sin(x)]=cos(x)$. However, if we want to instead interpret inputs as degrees we would instead have $fracddx[sin(x)]=fracpi180cos(x)$. See this question.
– JMoravitz
Aug 27 at 17:17
It is generally preferred in the mathematical community to use radians as it makes several calculations "nicer." For example, in calculus if we interpret $sin(x)$ and $cos(x)$ as taking inputs in terms of amounts of radians we have the derivative of $sin$ being $fracddx[sin(x)]=cos(x)$. However, if we want to instead interpret inputs as degrees we would instead have $fracddx[sin(x)]=fracpi180cos(x)$. See this question.
– JMoravitz
Aug 27 at 17:17
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
5
down vote
accepted
This mnemonic isn't inherently in any specific unit for measuring angles. The sine is $3/5$; that's not a convention of units, just an objective fact. Now, if you run it through an inverse sine calculator, it'll return an answer in whatever units it's designed to. Calculators typically have degree, radian and grad conventions you can switch herein. And that convention is used when interpreting what angle you'd like the sine of, if you ask for it. If $sin 30$ comes out as $0.5$, you're working in degrees. But that's all it is, a convention.
answered Aug 27 at 17:16
J.G.
14.1k11525
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
This mnemonic isn't inherently in any specific unit for measuring angles. The sine is $3/5$; that's not a convention of units, just an objective fact. Now, if you run it through an inverse sine calculator, it'll return an answer in whatever units it's designed to. Calculators typically have degree, radian and grad conventions you can switch herein. And that convention is used when interpreting what angle you'd like the sine of, if you ask for it. If $sin 30$ comes out as $0.5$, you're working in degrees. But that's all it is, a convention.
answered Aug 27 at 17:16
J.G.
14.1k11525
add a comment |Â
up vote
5
down vote
accepted
This mnemonic isn't inherently in any specific unit for measuring angles. The sine is $3/5$; that's not a convention of units, just an objective fact. Now, if you run it through an inverse sine calculator, it'll return an answer in whatever units it's designed to. Calculators typically have degree, radian and grad conventions you can switch herein. And that convention is used when interpreting what angle you'd like the sine of, if you ask for it. If $sin 30$ comes out as $0.5$, you're working in degrees. But that's all it is, a convention.
answered Aug 27 at 17:16
J.G.
14.1k11525
add a comment |Â
up vote
5
down vote
accepted
up vote
5
down vote
accepted
This mnemonic isn't inherently in any specific unit for measuring angles. The sine is $3/5$; that's not a convention of units, just an objective fact. Now, if you run it through an inverse sine calculator, it'll return an answer in whatever units it's designed to. Calculators typically have degree, radian and grad conventions you can switch herein. And that convention is used when interpreting what angle you'd like the sine of, if you ask for it. If $sin 30$ comes out as $0.5$, you're working in degrees. But that's all it is, a convention.
answered Aug 27 at 17:16
J.G.
14.1k11525
This mnemonic isn't inherently in any specific unit for measuring angles. The sine is $3/5$; that's not a convention of units, just an objective fact. Now, if you run it through an inverse sine calculator, it'll return an answer in whatever units it's designed to. Calculators typically have degree, radian and grad conventions you can switch herein. And that convention is used when interpreting what angle you'd like the sine of, if you ask for it. If $sin 30$ comes out as $0.5$, you're working in degrees. But that's all it is, a convention.
answered Aug 27 at 17:16
J.G.
14.1k11525
answered Aug 27 at 17:16
J.G.
14.1k11525
answered Aug 27 at 17:16
J.G.
14.1k11525
answered Aug 27 at 17:16
J.G.
14.1k11525
14.1k11525
add a comment |Â
add a comment |Â
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Mostly radians, sometimes degrees.
– Love Invariants
Aug 27 at 17:09
1
The result of your calculation is going to depend on whether your calculator is in degrees or radians. SOH CAH TOA, though, is independent of radians or degrees, because it is going the other way.
– Adrian Keister
Aug 27 at 17:09
4
Sine of an angle is opposite length over hypotenuse, regardless of what units the angle is in. But you will need to decide what units you want to use to compute $sin^-1(3/5)$
– ziggurism
Aug 27 at 17:10
3
The resulting number is an angle. Angles do not inherently by themselves have a preferred unit of measurement, just like how length does not have a preference for meters versus feet. How you interpret that angle depends on what you want. If you want the result to be in radians then you have an answer of about $0.643$ (rad). If you want the result to be in degrees then you have an answer of about $36.87^circ$
– JMoravitz
Aug 27 at 17:11
It is generally preferred in the mathematical community to use radians as it makes several calculations "nicer." For example, in calculus if we interpret $sin(x)$ and $cos(x)$ as taking inputs in terms of amounts of radians we have the derivative of $sin$ being $fracddx[sin(x)]=cos(x)$. However, if we want to instead interpret inputs as degrees we would instead have $fracddx[sin(x)]=fracpi180cos(x)$. See this question.
– JMoravitz
Aug 27 at 17:17