Trignometry applications of trig identities calc. Qs (1 Viewer)

Fiction · Mar 17, 2015

? http://imgur.com/bvOXkAi
~~Can someone take me through q5 step by step?~~
Can someone take me through q 6 c) and 7please?
Thankies

)

photastic · Mar 17, 2015

Fiction · Mar 17, 2015

Thank you!
You must spread some reputation around before giving it to photostic again

InteGrand · Mar 17, 2015

Fiction said:
? http://imgur.com/bvOXkAi
~~Can someone take me through q5 step by step?~~
Can someone take me through q 6 c) and 7please?
Thankies)

Q.7: $\sin x \cos x = \frac{1}{2}\times 2\sin x \cos x = \frac{1}{2}\sin 2x$ , which cannot exceed $\frac{1}{2}$ as $\sin 2x$ cannot exceed 1.

InteGrand · Mar 17, 2015

For Question 6 c), you should be able to see from your sketch that the two graphs are reflections of each other about the line $y=\frac{1}{2}$ , so the sum of y-values of the graphs at any point is 1, so $\frac{1}{2}(1+\cos 2x) + \frac{1}{2}(1-\cos 2x)=1$ (don't need a graph to see this actually – just expand the LHS).

But $\cos^2 x = \frac{1}{2}(1+\cos 2x)$ and $\sin ^2 x = \frac{1}{2}(1-\cos 2x)$ (these come from rearranging the double angle formula for cos: $\cos 2x = 2\cos^2 x -1 = 1 - 2\sin ^2 x$ ).

This means that $\sin^2 x + \cos^2 x = 1$ .

Fiction · Mar 17, 2015

InteGrand said:
Q.7: $\sin x \cos x = \frac{1}{2}\times 2\sin x \cos x = \frac{1}{2}\sin 2x$ , which cannot exceed $\frac{1}{2}$ as $\sin 2x$ cannot exceed 1.

InteGrand said:
For Question 6 c), you should be able to see from your sketch that the two graphs are reflections of each other about the line $y=\frac{1}{2}$ , so the sum of y-values of the graphs at any point is 1, so $\frac{1}{2}(1+\cos 2x) + \frac{1}{2}(1-\cos 2x)=1$ (don't need a graph to see this actually – just expand the LHS).

But $\cos^2 x = \frac{1}{2}(1+\cos 2x)$ and $\sin ^2 x = \frac{1}{2}(1-\cos 2x)$ (these come from rearranging the double angle formula for cos: $\cos 2x = 2\cos^2 x -1 = 1 - 2\sin ^2 x$ ).

This means that $\sin^2 x + \cos^2 x = 1$ .

Thank you! C:
Lol I think my rep button is broken, I don't recall repping you in the near past but 'you must spread some rep around before giving it to integrand again'

Trignometry applications of trig identities calc. Qs (1 Viewer)

Fiction

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photastic

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InteGrand

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InteGrand

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Fiction

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