A maths: some questions to clarify

bonkysleuth SG

Find the range of values of x between 0 and pi inclusive which satisfies

sin x/2 > 0.5

cos 2x < 0

Hence state the range of values of x between 0 and pi inclusive which satisfies both inequalities.

Totally no idea what the question is asking for. Though I have a brief idea of what the answer should be. Would be great if someone shows me the proper and correct method of doing.

4^(x+0.5) = 7(2^x) - 5

Got x = 1.32 and 0. But answer only has 1.32.... i wonder why we must reject 0? I substituted it into the equation and both are perfectly fine.

3. sin a = -2/3

cos b = 2/7 and a and b lie within the same quadrant. Find the exact value of

cos b/2

Shouldn't there be both a postitive and negative answer? However my answer booklet only stated the negative answer. Why should we reject the positive answer? thanks.

Mikethm SG

To understand, you should sketch the graph of y = sin (x/2) and see the domain for which the graph is above 0.5. Same for y = cos 2x except you want the domain for which the graph is below the x-axis.

Following that, you want to take the domain which satisfy both. aka the common region.

Perhaps you can post the original full question?

a and b lies in the last quadrant. This means that

270<b<360

135<(b/2)<180

Since b/2 is in the 2nd quadrant, cos(b/2) has to be -ve.