How to solve $cos(theta + angle)$ equation?
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I can't seem to figure out how to solve an equation similar to the one below.
$$cos(theta+fracpi3)=frac1sqrt3$$
The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.
$$theta+fracpi3=arccos(frac1sqrt3)$$
Am I missing a step when solving this equation?
trigonometry
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up vote
1
down vote
favorite
I can't seem to figure out how to solve an equation similar to the one below.
$$cos(theta+fracpi3)=frac1sqrt3$$
The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.
$$theta+fracpi3=arccos(frac1sqrt3)$$
Am I missing a step when solving this equation?
trigonometry
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I can't seem to figure out how to solve an equation similar to the one below.
$$cos(theta+fracpi3)=frac1sqrt3$$
The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.
$$theta+fracpi3=arccos(frac1sqrt3)$$
Am I missing a step when solving this equation?
trigonometry
I can't seem to figure out how to solve an equation similar to the one below.
$$cos(theta+fracpi3)=frac1sqrt3$$
The steps I have taken so far are shown below. From there I would just solve for $theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.
$$theta+fracpi3=arccos(frac1sqrt3)$$
Am I missing a step when solving this equation?
trigonometry
asked Aug 11 at 0:36
Matt Hough
323
323
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2 Answers
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Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
1
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
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$$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$
Try going off of this.
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
1
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
add a comment |Â
up vote
1
down vote
accepted
Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
1
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)
Your step is ok, but it misses the "second" solution: $$theta+fracpi3=pmarccos(frac1sqrt3)$$
Move the $pi/3$ over and you are done! (You may add the multiplicity of $2pi$ if needed)
answered Aug 11 at 0:44
imranfat
7,94441432
7,94441432
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
1
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
add a comment |Â
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
1
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
Thanks for the answer. I don't quite understand why it would be $pm$, could you please explain that?
â Matt Hough
Aug 11 at 2:06
1
1
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
Remember that cosine is periodic and for any number in $(0, 1)$ one of the angles whose cosine is that number is plus while the other is minus. Check the unit circle!
â Sean Roberson
Aug 11 at 3:04
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
@SeanRoberson Ahh yep I see. Thanks for that.
â Matt Hough
Aug 11 at 4:45
add a comment |Â
up vote
0
down vote
$$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$
Try going off of this.
add a comment |Â
up vote
0
down vote
$$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$
Try going off of this.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
$$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$
Try going off of this.
$$cos(a+b) = cos acos b - sin asin b$$$$=costhetacosfracpi 3 - sinthetasinfracpi 3$$
Try going off of this.
answered Aug 11 at 0:45
Rushabh Mehta
1,287216
1,287216
add a comment |Â
add a comment |Â
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