How do I determine the sign of “a” in a trig function?
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So tomorrow I have a quiz regarding trigonometric functions. The following is a practice question for that exam:
How do I determine "a" without inserting t or y values into the equation?
I would do 111/2, but this would give me 55.5, and the answer should be -55.5. Someone please explain.
trigonometry
asked Nov 15 at 0:09
Brian Blumberg
11911
add a comment |
up vote
-1
down vote
favorite
So tomorrow I have a quiz regarding trigonometric functions. The following is a practice question for that exam:
How do I determine "a" without inserting t or y values into the equation?
I would do 111/2, but this would give me 55.5, and the answer should be -55.5. Someone please explain.
trigonometry
asked Nov 15 at 0:09
Brian Blumberg
11911
From 3a, we can substitute $t = 8$ and $h(t)=117$ into the equation. Then solving for $a$ yields $a = -55.5$.
– suchan
Nov 15 at 0:18
I do recognize that, but I do not want to do subsitution, what if I were not given the equation, how would I approach the question?
– Brian Blumberg
Nov 15 at 0:19
1
If you were not given the equation, what would be the meaning of the task "Find the value of $a$"?
– suchan
Nov 15 at 0:21
"A seat starts at the bottom of the wheel", so $a$ must be negative since $h(0) = 61.5 + a$.
– Bungo
Nov 15 at 0:41
If the wheel would start at the highest point, you would have $a = +55.5$. However, the wheel starts at the lowest point, hence $a = -55.5$.
– M. Wind
Nov 15 at 0:43
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
So tomorrow I have a quiz regarding trigonometric functions. The following is a practice question for that exam:
How do I determine "a" without inserting t or y values into the equation?
I would do 111/2, but this would give me 55.5, and the answer should be -55.5. Someone please explain.
trigonometry
asked Nov 15 at 0:09
Brian Blumberg
11911
So tomorrow I have a quiz regarding trigonometric functions. The following is a practice question for that exam:
How do I determine "a" without inserting t or y values into the equation?
I would do 111/2, but this would give me 55.5, and the answer should be -55.5. Someone please explain.
trigonometry
trigonometry
asked Nov 15 at 0:09
Brian Blumberg
11911
asked Nov 15 at 0:09
Brian Blumberg
11911
asked Nov 15 at 0:09
Brian Blumberg
11911
asked Nov 15 at 0:09
Brian Blumberg
11911
asked Nov 15 at 0:09
Brian Blumberg
11911
11911
From 3a, we can substitute $t = 8$ and $h(t)=117$ into the equation. Then solving for $a$ yields $a = -55.5$.
– suchan
Nov 15 at 0:18
I do recognize that, but I do not want to do subsitution, what if I were not given the equation, how would I approach the question?
– Brian Blumberg
Nov 15 at 0:19
1
If you were not given the equation, what would be the meaning of the task "Find the value of $a$"?
– suchan
Nov 15 at 0:21
"A seat starts at the bottom of the wheel", so $a$ must be negative since $h(0) = 61.5 + a$.
– Bungo
Nov 15 at 0:41
If the wheel would start at the highest point, you would have $a = +55.5$. However, the wheel starts at the lowest point, hence $a = -55.5$.
– M. Wind
Nov 15 at 0:43
add a comment |
From 3a, we can substitute $t = 8$ and $h(t)=117$ into the equation. Then solving for $a$ yields $a = -55.5$.
– suchan
Nov 15 at 0:18
I do recognize that, but I do not want to do subsitution, what if I were not given the equation, how would I approach the question?
– Brian Blumberg
Nov 15 at 0:19
1
If you were not given the equation, what would be the meaning of the task "Find the value of $a$"?
– suchan
Nov 15 at 0:21
"A seat starts at the bottom of the wheel", so $a$ must be negative since $h(0) = 61.5 + a$.
– Bungo
Nov 15 at 0:41
If the wheel would start at the highest point, you would have $a = +55.5$. However, the wheel starts at the lowest point, hence $a = -55.5$.
– M. Wind
Nov 15 at 0:43
From 3a, we can substitute $t = 8$ and $h(t)=117$ into the equation. Then solving for $a$ yields $a = -55.5$.
– suchan
Nov 15 at 0:18
From 3a, we can substitute $t = 8$ and $h(t)=117$ into the equation. Then solving for $a$ yields $a = -55.5$.
– suchan
Nov 15 at 0:18
I do recognize that, but I do not want to do subsitution, what if I were not given the equation, how would I approach the question?
– Brian Blumberg
Nov 15 at 0:19
I do recognize that, but I do not want to do subsitution, what if I were not given the equation, how would I approach the question?
– Brian Blumberg
Nov 15 at 0:19
1
1
If you were not given the equation, what would be the meaning of the task "Find the value of $a$"?
– suchan
Nov 15 at 0:21
If you were not given the equation, what would be the meaning of the task "Find the value of $a$"?
– suchan
Nov 15 at 0:21
"A seat starts at the bottom of the wheel", so $a$ must be negative since $h(0) = 61.5 + a$.
– Bungo
Nov 15 at 0:41
"A seat starts at the bottom of the wheel", so $a$ must be negative since $h(0) = 61.5 + a$.
– Bungo
Nov 15 at 0:41
If the wheel would start at the highest point, you would have $a = +55.5$. However, the wheel starts at the lowest point, hence $a = -55.5$.
– M. Wind
Nov 15 at 0:43
If the wheel would start at the highest point, you would have $a = +55.5$. However, the wheel starts at the lowest point, hence $a = -55.5$.
– M. Wind
Nov 15 at 0:43
add a comment |
1 Answer
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When using $cos$ (and $sin$) to describe the coordinates of circular motion (like you do here, describing the $y$-coordinate), the number in front of the trigonometric function (in this case $a$) is the radius of the circle. So $111/2=55.5$, just as you've done.
The sign depends on whether you begin on the top or on the bottom. When you begin your journey around the wheel, we have $t=0$. Inserting that makes the value of $cos(pi t/8)$ equal $1$. So now is the question: Do you want to start at height $61.5+55.5$, or at height $61.5-55.5$?
Yes, I think you should solve this by inserting values for $t$ and $y$, even though it looks like you want to avoid it. But inserting $0$ into a cosine barely counts in my opinion. And the whole point of existence for an equation like that is to insert values and calculate. So why are you really so bent on not doing it?
answered Nov 15 at 0:29
Arthur
108k7103186
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
When using $cos$ (and $sin$) to describe the coordinates of circular motion (like you do here, describing the $y$-coordinate), the number in front of the trigonometric function (in this case $a$) is the radius of the circle. So $111/2=55.5$, just as you've done.
The sign depends on whether you begin on the top or on the bottom. When you begin your journey around the wheel, we have $t=0$. Inserting that makes the value of $cos(pi t/8)$ equal $1$. So now is the question: Do you want to start at height $61.5+55.5$, or at height $61.5-55.5$?
Yes, I think you should solve this by inserting values for $t$ and $y$, even though it looks like you want to avoid it. But inserting $0$ into a cosine barely counts in my opinion. And the whole point of existence for an equation like that is to insert values and calculate. So why are you really so bent on not doing it?
answered Nov 15 at 0:29
Arthur
108k7103186
add a comment |
up vote
0
down vote
When using $cos$ (and $sin$) to describe the coordinates of circular motion (like you do here, describing the $y$-coordinate), the number in front of the trigonometric function (in this case $a$) is the radius of the circle. So $111/2=55.5$, just as you've done.
The sign depends on whether you begin on the top or on the bottom. When you begin your journey around the wheel, we have $t=0$. Inserting that makes the value of $cos(pi t/8)$ equal $1$. So now is the question: Do you want to start at height $61.5+55.5$, or at height $61.5-55.5$?
Yes, I think you should solve this by inserting values for $t$ and $y$, even though it looks like you want to avoid it. But inserting $0$ into a cosine barely counts in my opinion. And the whole point of existence for an equation like that is to insert values and calculate. So why are you really so bent on not doing it?
answered Nov 15 at 0:29
Arthur
108k7103186
add a comment |
up vote
0
down vote
up vote
0
down vote
When using $cos$ (and $sin$) to describe the coordinates of circular motion (like you do here, describing the $y$-coordinate), the number in front of the trigonometric function (in this case $a$) is the radius of the circle. So $111/2=55.5$, just as you've done.
The sign depends on whether you begin on the top or on the bottom. When you begin your journey around the wheel, we have $t=0$. Inserting that makes the value of $cos(pi t/8)$ equal $1$. So now is the question: Do you want to start at height $61.5+55.5$, or at height $61.5-55.5$?
Yes, I think you should solve this by inserting values for $t$ and $y$, even though it looks like you want to avoid it. But inserting $0$ into a cosine barely counts in my opinion. And the whole point of existence for an equation like that is to insert values and calculate. So why are you really so bent on not doing it?
answered Nov 15 at 0:29
Arthur
108k7103186
When using $cos$ (and $sin$) to describe the coordinates of circular motion (like you do here, describing the $y$-coordinate), the number in front of the trigonometric function (in this case $a$) is the radius of the circle. So $111/2=55.5$, just as you've done.
The sign depends on whether you begin on the top or on the bottom. When you begin your journey around the wheel, we have $t=0$. Inserting that makes the value of $cos(pi t/8)$ equal $1$. So now is the question: Do you want to start at height $61.5+55.5$, or at height $61.5-55.5$?
Yes, I think you should solve this by inserting values for $t$ and $y$, even though it looks like you want to avoid it. But inserting $0$ into a cosine barely counts in my opinion. And the whole point of existence for an equation like that is to insert values and calculate. So why are you really so bent on not doing it?
answered Nov 15 at 0:29
Arthur
108k7103186
edited Nov 15 at 0:42
answered Nov 15 at 0:29
Arthur
108k7103186
answered Nov 15 at 0:29
Arthur
108k7103186
answered Nov 15 at 0:29
Arthur
108k7103186
108k7103186
add a comment |
add a comment |
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From 3a, we can substitute $t = 8$ and $h(t)=117$ into the equation. Then solving for $a$ yields $a = -55.5$.
– suchan
Nov 15 at 0:18
I do recognize that, but I do not want to do subsitution, what if I were not given the equation, how would I approach the question?
– Brian Blumberg
Nov 15 at 0:19
1
If you were not given the equation, what would be the meaning of the task "Find the value of $a$"?
– suchan
Nov 15 at 0:21
"A seat starts at the bottom of the wheel", so $a$ must be negative since $h(0) = 61.5 + a$.
– Bungo
Nov 15 at 0:41
If the wheel would start at the highest point, you would have $a = +55.5$. However, the wheel starts at the lowest point, hence $a = -55.5$.
– M. Wind
Nov 15 at 0:43