Solve for a value (Trig question)
$begingroup$
The question is phrased as, in the triangle $xyz$, $cos(x)=sin(z)$. If $x=3j-19$ and $z=5j-15$, what is the value of $j$?
Firstly, I'm not quite sure if the variables refer to the side length or the angle measurements.
I'm sure there's an identity that will solve this question in 1 step but I'm not sure which one it would be. I want to use sine law but that seems to only give me $$frac{sin(x)}{3j-19}=frac{cos(x)}{5j-15}$$
which doesn't seem helpful?
trigonometry
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
asked Dec 24 '18 at 8:23
SatSat
405
$endgroup$
add a comment |
$begingroup$
The question is phrased as, in the triangle $xyz$, $cos(x)=sin(z)$. If $x=3j-19$ and $z=5j-15$, what is the value of $j$?
Firstly, I'm not quite sure if the variables refer to the side length or the angle measurements.
I'm sure there's an identity that will solve this question in 1 step but I'm not sure which one it would be. I want to use sine law but that seems to only give me $$frac{sin(x)}{3j-19}=frac{cos(x)}{5j-15}$$
which doesn't seem helpful?
trigonometry
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
asked Dec 24 '18 at 8:23
SatSat
405
$endgroup$
$begingroup$
Are $x$ and $z$ in degree or radian?
$endgroup$
– Mythomorphic
Dec 24 '18 at 8:33
add a comment |
$begingroup$
The question is phrased as, in the triangle $xyz$, $cos(x)=sin(z)$. If $x=3j-19$ and $z=5j-15$, what is the value of $j$?
Firstly, I'm not quite sure if the variables refer to the side length or the angle measurements.
I'm sure there's an identity that will solve this question in 1 step but I'm not sure which one it would be. I want to use sine law but that seems to only give me $$frac{sin(x)}{3j-19}=frac{cos(x)}{5j-15}$$
which doesn't seem helpful?
trigonometry
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
asked Dec 24 '18 at 8:23
SatSat
405
$endgroup$
The question is phrased as, in the triangle $xyz$, $cos(x)=sin(z)$. If $x=3j-19$ and $z=5j-15$, what is the value of $j$?
Firstly, I'm not quite sure if the variables refer to the side length or the angle measurements.
I'm sure there's an identity that will solve this question in 1 step but I'm not sure which one it would be. I want to use sine law but that seems to only give me $$frac{sin(x)}{3j-19}=frac{cos(x)}{5j-15}$$
which doesn't seem helpful?
trigonometry
trigonometry
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
asked Dec 24 '18 at 8:23
SatSat
405
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
asked Dec 24 '18 at 8:23
SatSat
405
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
edited Dec 24 '18 at 8:31
Mythomorphic
5,3491834
5,3491834
asked Dec 24 '18 at 8:23
SatSat
405
asked Dec 24 '18 at 8:23
SatSat
405
asked Dec 24 '18 at 8:23
SatSat
405
405
$begingroup$
Are $x$ and $z$ in degree or radian?
$endgroup$
– Mythomorphic
Dec 24 '18 at 8:33
add a comment |
$begingroup$
Are $x$ and $z$ in degree or radian?
$endgroup$
– Mythomorphic
Dec 24 '18 at 8:33
$begingroup$
Are $x$ and $z$ in degree or radian?
$endgroup$
– Mythomorphic
Dec 24 '18 at 8:33
$begingroup$
Are $x$ and $z$ in degree or radian?
$endgroup$
– Mythomorphic
Dec 24 '18 at 8:33
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Usually, angles and sides are distinguishable by capital and lowercase letters. Here, $x$ and $y$ refer to angle measures.
Recalling $cos theta = sin (90-theta)$ in the first quadrant, you can conclude $cos x = sin z$ if $x+z = 90$, resulting in
$$3j-19+(5j-15) = 90 iff 8j-34 = 90 iff 8j = 124 iff j = 15.5$$
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
$endgroup$
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
add a comment |
$begingroup$
Hint:
Use the identity
$$cos(90^circ-A)=sin A$$
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
Usually, angles and sides are distinguishable by capital and lowercase letters. Here, $x$ and $y$ refer to angle measures.
Recalling $cos theta = sin (90-theta)$ in the first quadrant, you can conclude $cos x = sin z$ if $x+z = 90$, resulting in
$$3j-19+(5j-15) = 90 iff 8j-34 = 90 iff 8j = 124 iff j = 15.5$$
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
$endgroup$
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
add a comment |
$begingroup$
Usually, angles and sides are distinguishable by capital and lowercase letters. Here, $x$ and $y$ refer to angle measures.
Recalling $cos theta = sin (90-theta)$ in the first quadrant, you can conclude $cos x = sin z$ if $x+z = 90$, resulting in
$$3j-19+(5j-15) = 90 iff 8j-34 = 90 iff 8j = 124 iff j = 15.5$$
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
$endgroup$
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
add a comment |
$begingroup$
Usually, angles and sides are distinguishable by capital and lowercase letters. Here, $x$ and $y$ refer to angle measures.
Recalling $cos theta = sin (90-theta)$ in the first quadrant, you can conclude $cos x = sin z$ if $x+z = 90$, resulting in
$$3j-19+(5j-15) = 90 iff 8j-34 = 90 iff 8j = 124 iff j = 15.5$$
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
$endgroup$
Usually, angles and sides are distinguishable by capital and lowercase letters. Here, $x$ and $y$ refer to angle measures.
Recalling $cos theta = sin (90-theta)$ in the first quadrant, you can conclude $cos x = sin z$ if $x+z = 90$, resulting in
$$3j-19+(5j-15) = 90 iff 8j-34 = 90 iff 8j = 124 iff j = 15.5$$
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
answered Dec 24 '18 at 8:38
KM101KM101
6,0901525
6,0901525
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
add a comment |
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
$begingroup$
Yes, that's it. I knew there was some identity that I was missing.
$endgroup$
– Sat
Dec 24 '18 at 8:43
add a comment |
$begingroup$
Hint:
Use the identity
$$cos(90^circ-A)=sin A$$
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
$endgroup$
add a comment |
$begingroup$
Hint:
Use the identity
$$cos(90^circ-A)=sin A$$
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
$endgroup$
add a comment |
$begingroup$
Hint:
Use the identity
$$cos(90^circ-A)=sin A$$
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
$endgroup$
Hint:
Use the identity
$$cos(90^circ-A)=sin A$$
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
answered Dec 24 '18 at 8:36
MythomorphicMythomorphic
5,3491834
5,3491834
add a comment |
add a comment |
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$begingroup$
Are $x$ and $z$ in degree or radian?
$endgroup$
– Mythomorphic
Dec 24 '18 at 8:33