Solve on the interval $[0,2pi)$: $4 sin(x) cos(x)=1$. [closed]
I tried using the product-to-sum formulas, but did not come up with the correct answer.
algebra-precalculus trigonometry
edited Nov 29 at 10:52
amWhy
191k28224439
asked Nov 29 at 0:39
math818
33
closed as off-topic by Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos Nov 29 at 12:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
I tried using the product-to-sum formulas, but did not come up with the correct answer.
algebra-precalculus trigonometry
edited Nov 29 at 10:52
amWhy
191k28224439
asked Nov 29 at 0:39
math818
33
closed as off-topic by Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos Nov 29 at 12:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
I tried using the product-to-sum formulas, but did not come up with the correct answer.
algebra-precalculus trigonometry
edited Nov 29 at 10:52
amWhy
191k28224439
asked Nov 29 at 0:39
math818
33
I tried using the product-to-sum formulas, but did not come up with the correct answer.
algebra-precalculus trigonometry
algebra-precalculus trigonometry
edited Nov 29 at 10:52
amWhy
191k28224439
asked Nov 29 at 0:39
math818
33
edited Nov 29 at 10:52
amWhy
191k28224439
asked Nov 29 at 0:39
math818
33
edited Nov 29 at 10:52
amWhy
191k28224439
edited Nov 29 at 10:52
amWhy
191k28224439
edited Nov 29 at 10:52
amWhy
191k28224439
191k28224439
asked Nov 29 at 0:39
math818
33
asked Nov 29 at 0:39
math818
33
asked Nov 29 at 0:39
math818
33
33
closed as off-topic by Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos Nov 29 at 12:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos Nov 29 at 12:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, amWhy, Toby Mak, Delta-u, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
As was hinted, $$sin2x=2sin xcos x$$
Hence, your equation becomes
$$2sin2x=1$$
$$sin2x=frac12$$
$$2x=arcsinfrac12$$
$$2x=fracpi6,,frac{5pi}6$$
$$x=fracpi{12},,frac{5pi}{12}$$
answered Nov 29 at 1:36
clathratus
2,862328
add a comment |
Hint: use the double-angle formula for sine:
$$sin(2theta) = 2sin(theta)cos(theta)$$
edited Nov 29 at 0:42
Bernard
117k638111
answered Nov 29 at 0:40
Eevee Trainer
3,462326
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
As was hinted, $$sin2x=2sin xcos x$$
Hence, your equation becomes
$$2sin2x=1$$
$$sin2x=frac12$$
$$2x=arcsinfrac12$$
$$2x=fracpi6,,frac{5pi}6$$
$$x=fracpi{12},,frac{5pi}{12}$$
answered Nov 29 at 1:36
clathratus
2,862328
add a comment |
As was hinted, $$sin2x=2sin xcos x$$
Hence, your equation becomes
$$2sin2x=1$$
$$sin2x=frac12$$
$$2x=arcsinfrac12$$
$$2x=fracpi6,,frac{5pi}6$$
$$x=fracpi{12},,frac{5pi}{12}$$
answered Nov 29 at 1:36
clathratus
2,862328
add a comment |
As was hinted, $$sin2x=2sin xcos x$$
Hence, your equation becomes
$$2sin2x=1$$
$$sin2x=frac12$$
$$2x=arcsinfrac12$$
$$2x=fracpi6,,frac{5pi}6$$
$$x=fracpi{12},,frac{5pi}{12}$$
answered Nov 29 at 1:36
clathratus
2,862328
As was hinted, $$sin2x=2sin xcos x$$
Hence, your equation becomes
$$2sin2x=1$$
$$sin2x=frac12$$
$$2x=arcsinfrac12$$
$$2x=fracpi6,,frac{5pi}6$$
$$x=fracpi{12},,frac{5pi}{12}$$
answered Nov 29 at 1:36
clathratus
2,862328
edited Nov 29 at 1:55
answered Nov 29 at 1:36
clathratus
2,862328
answered Nov 29 at 1:36
clathratus
2,862328
answered Nov 29 at 1:36
clathratus
2,862328
2,862328
add a comment |
add a comment |
Hint: use the double-angle formula for sine:
$$sin(2theta) = 2sin(theta)cos(theta)$$
edited Nov 29 at 0:42
Bernard
117k638111
answered Nov 29 at 0:40
Eevee Trainer
3,462326
add a comment |
Hint: use the double-angle formula for sine:
$$sin(2theta) = 2sin(theta)cos(theta)$$
edited Nov 29 at 0:42
Bernard
117k638111
answered Nov 29 at 0:40
Eevee Trainer
3,462326
add a comment |
Hint: use the double-angle formula for sine:
$$sin(2theta) = 2sin(theta)cos(theta)$$
edited Nov 29 at 0:42
Bernard
117k638111
answered Nov 29 at 0:40
Eevee Trainer
3,462326
Hint: use the double-angle formula for sine:
$$sin(2theta) = 2sin(theta)cos(theta)$$
edited Nov 29 at 0:42
Bernard
117k638111
answered Nov 29 at 0:40
Eevee Trainer
3,462326
edited Nov 29 at 0:42
Bernard
117k638111
edited Nov 29 at 0:42
Bernard
117k638111
edited Nov 29 at 0:42
Bernard
117k638111
117k638111
answered Nov 29 at 0:40
Eevee Trainer
3,462326
answered Nov 29 at 0:40
Eevee Trainer
3,462326
answered Nov 29 at 0:40
Eevee Trainer
3,462326
3,462326
add a comment |
add a comment |
