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# Exam Question stuck: Logs @ Sine/cos/tan rules watch

1. I am stuck on these questions and don't know what to do... I am not sure about the starting steps
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2. Here are some hints:

For question 7, notice that for a product of two brackets to equal zero, either of the brackets must equal zero. And remember that sin θ / cos θ = tan θ.

For question 9a, you have to use the trapezium rule, 1/2 h [f(0) + f(1) + 2(f(0.25) + f(0.5) + f(0.75))], where f(x) = log(x^2 + 1).

9b is a simple transation by a vector. The rule is that if y in the original equation becomes y - k in the new equation, the curve has been translated by vector [0, k].

9c is mostly use of log rules, which are
log(ab) = log a + log b
log(a/b) = log a - log b
log x^n = n log x.

Let me know where in particular you are stuck.
3. (Original post by mike256)
Here are some hints:

For question 7, notice that for a product of two brackets to equal zero, either of the brackets must equal zero. And remember that sin θ / cos θ = tan θ.

For question 9a, you have to use the trapezium rule, 1/2 h [f(0) + f(1) + 2(f(0.25) + f(0.5) + f(0.75))], where f(x) = log(x^2 + 1).

9b is a simple transation by a vector. The rule is that if y in the original equation becomes y - k in the new equation, the curve has been translated by vector [0, k].

9c is mostly use of log rules, which are
log(ab) = log a + log b
log(a/b) = log a - log b
log x^n = n log x.

Let me know where in particular you are stuck.
I am stuck because the log10 is putting me off and I can only do simple log work...
4. (Original post by Freddy12345)
I am stuck because the log10 is putting me off and I can only do simple log work...
log10 means logarithm to base 10, i.e.

means that

It behaves like all other logarithms.

Which part of the question are you stuck on?
5. (Original post by mike256)
log10 means logarithm to base 10, i.e.

means that

It behaves like all other logarithms.

Which part of the question are you stuck on?
First part says use trapezium rule, does that mean I have to integrate first, or use trapezium rule straightaway?

Also Part c (ii) 4 mark question, both equations are the same, so I don't understand what's going on there.
6. (Original post by Freddy12345)
First part says use trapezium rule, does that mean I have to integrate first, or use trapezium rule straightaway?

Also Part c (ii) 4 mark question, both equations are the same, so I don't understand what's going on there.
The trapezium rule is for estimating the integral, so you don't integrate the equation first (we wouldn't be able to integrate logs with only Core 2 knowledge).

For part (c)(ii), the second equation has a 1 added to it. Because you need to show that the transformation is a stretch, you want to rearrange the equation

y = 1 + 2log10 x

so that it is in the form

y = 2log10(kx), where k is some stretch factor.

Start by rewriting it as

y = log10 10 + 2log10 x, because 1 = log1010.

The difficult part is to realise that you need to somehow combine the terms log1010 + 2log10x. You could use the rule that log a + log b = log(ab), but that only works if the coefficients of the logs are the same, so you need to rewrite log10 10 as 2 log (something). Hint: use the fact that 2log a = log a2.

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