How do I find the value of the trig functions listed below?
$begingroup$
How do I find the value of trig functions listed below? I need to express the answer in radical form.
a) tan(5π/12)
b) cos(-π/12)
c) sin(π/8)
Do I use the half angle identity to solve c? I'm confused of the others.
algebra-precalculus
asked Dec 11 '18 at 2:13
User231User231
105
$endgroup$
add a comment |
$begingroup$
How do I find the value of trig functions listed below? I need to express the answer in radical form.
a) tan(5π/12)
b) cos(-π/12)
c) sin(π/8)
Do I use the half angle identity to solve c? I'm confused of the others.
algebra-precalculus
asked Dec 11 '18 at 2:13
User231User231
105
$endgroup$
add a comment |
$begingroup$
How do I find the value of trig functions listed below? I need to express the answer in radical form.
a) tan(5π/12)
b) cos(-π/12)
c) sin(π/8)
Do I use the half angle identity to solve c? I'm confused of the others.
algebra-precalculus
asked Dec 11 '18 at 2:13
User231User231
105
$endgroup$
How do I find the value of trig functions listed below? I need to express the answer in radical form.
a) tan(5π/12)
b) cos(-π/12)
c) sin(π/8)
Do I use the half angle identity to solve c? I'm confused of the others.
algebra-precalculus
algebra-precalculus
asked Dec 11 '18 at 2:13
User231User231
105
asked Dec 11 '18 at 2:13
User231User231
105
asked Dec 11 '18 at 2:13
User231User231
105
asked Dec 11 '18 at 2:13
User231User231
105
asked Dec 11 '18 at 2:13
User231User231
105
105
add a comment |
add a comment |
1 Answer
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$begingroup$
Yes, if you're working from the standard known values, it'll take a half-angle to reach $frac{pi}{8}$. For the others, $frac{5pi}{12}=frac{pi}{6}+frac{pi}{4}$ and $frac{-pi}{12}=frac{pi}{6}-frac{pi}{4}$, so angle addition identities will do it.
These are not values I have memorized; if I needed them, I'd use the identities myself.
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
$endgroup$
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
1
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes, if you're working from the standard known values, it'll take a half-angle to reach $frac{pi}{8}$. For the others, $frac{5pi}{12}=frac{pi}{6}+frac{pi}{4}$ and $frac{-pi}{12}=frac{pi}{6}-frac{pi}{4}$, so angle addition identities will do it.
These are not values I have memorized; if I needed them, I'd use the identities myself.
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
$endgroup$
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
1
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
add a comment |
$begingroup$
Yes, if you're working from the standard known values, it'll take a half-angle to reach $frac{pi}{8}$. For the others, $frac{5pi}{12}=frac{pi}{6}+frac{pi}{4}$ and $frac{-pi}{12}=frac{pi}{6}-frac{pi}{4}$, so angle addition identities will do it.
These are not values I have memorized; if I needed them, I'd use the identities myself.
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
$endgroup$
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
1
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
add a comment |
$begingroup$
Yes, if you're working from the standard known values, it'll take a half-angle to reach $frac{pi}{8}$. For the others, $frac{5pi}{12}=frac{pi}{6}+frac{pi}{4}$ and $frac{-pi}{12}=frac{pi}{6}-frac{pi}{4}$, so angle addition identities will do it.
These are not values I have memorized; if I needed them, I'd use the identities myself.
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
$endgroup$
Yes, if you're working from the standard known values, it'll take a half-angle to reach $frac{pi}{8}$. For the others, $frac{5pi}{12}=frac{pi}{6}+frac{pi}{4}$ and $frac{-pi}{12}=frac{pi}{6}-frac{pi}{4}$, so angle addition identities will do it.
These are not values I have memorized; if I needed them, I'd use the identities myself.
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
answered Dec 11 '18 at 2:37
jmerryjmerry
9,4881124
9,4881124
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
1
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
add a comment |
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
1
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
$begingroup$
We can also use the half-angle formulas to obtain $cos (5pi/12)$ and $sin (5pi/12)$ from $cos (5pi/6)$ to answer a) and b).
$endgroup$
– DanielWainfleet
Dec 11 '18 at 6:59
1
1
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
Sure. I'd rather go with the rational operations of the angle addition formulas than the square roots of the half-angle formulas if I have the choice, but that's an option too.
$endgroup$
– jmerry
Dec 11 '18 at 8:03
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
For the answer for the first one I got 2+3 radical 3 and the second radical 2+ radical 3 over 2.
$endgroup$
– User231
Dec 11 '18 at 14:44
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
$begingroup$
Wrong for both (a) and (b). The second fails the common-sense test that a cosine must be between $-1$ and $1$. If you want any more feedback than that, you'll have to show your work.
$endgroup$
– jmerry
Dec 11 '18 at 20:15
add a comment |
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