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Melody

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यूजर का नामMelody
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Melody  11 Feb 2022
 #2
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bbygrl1996:

If sin (30) = 1⁄2 then the cosine of what angle will be 1⁄2?



Walt's method will work fine. Thankyou for posting Walt, you gave a good answer,

But there are other methods that I would like to talk about.

I'd really like other people who have been introduced to trigonometry at school to also pay attention to this one.
Draw a right angled triangle. I really want you to do this.
mark one angle as 30degrees
since sine 30 = 1/2
You can put 1 on the opposite side and 2 on the Hypotenuse.
Now think for a bit.......
Can you 'see' the answer yet? That is cos of what angle = 1/2
If not maybe you should work out what the 3rd angle will be.
what is the cos of the 3rd angle?
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Now we'll do it more generally
right angled triangle.JPG
Consider this triangle.
what is the size of the 3rd angle (in terms of theta)
hopefully you wil realise that it is 90-theta

Now, on this triangle,
what is Sine (theta)
hopefully you know that it is t / Hyp
what is Cosine(90 - theta) answer t / Hyp
so
sine (theta) = cosine (90-theta)
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Did you ever think about why cosine is sine with a co out the front?

Have you heard of COMPLEMENTARY ANGLES.
These are angles that add up to 90degrees
e.g. 30degrees and 60degrees are complementary angles
85 degrees and 5 degrees are complementary angles

The 'co' stands for complementary.
sine(theta) = cos(90-theta)
sin -1 (t / H) + cos -1(t/H) = 90 degrees

I hope that a few people learn something from this one
6 Jan 2014
 #60
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Random260:

1a) 170000(1+0.066/3)^(3x5)
= $235620 (rounded to whole number)

1b) 170000(1+0.066/2)^(2x5)
= $235208

1c) 170000(1+ 0.006/1) ^ (1x5)
= $234010



Your first answer is good. It would be excellent except that you have cut corners again.
I want the formula and what each of the letters equal and then the substitution and then the answer.
I want these even though I didn't expressly ask for them.
I also want you to think every time about why t and n are equal to whatever they are equal to.
If you understand it properly and you keep reminding yourself about the relevance of what your are doing then it won't be hard to remember. (It will be obvious)

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You had me really confused about b and c. You didn't interprete my question the way i had intended. (It doesn't matter)
You thought I meant 6 years and as a separate question, 1/3 of a year.
Ok lets go with that. Your answers are not correct.
Always think about the key number. That is, if the interest is expressed yearly, which it nearly always is, how many compounding periods are there in a year.
for both of these the annual interest rate is the same as part 'a' and it is still compounded ever 4 months. Only the time that the money stays in the account is different.
Try them again.
This time don't cut corners.
and think about every step!
YOU CAN DO THIS.
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[size=150]Before you even start tell me in words[/size]
what does the r in the formula represent?
and
what does the n in the formula represent?
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Maybe if you are really thinking hard you could even tell me what questions you actually did answer. But this might be too hard.
5 Jan 2014