C2 Trignometry

Can someone please help on the following:

1 i) Express sin2x + cos(90-2x) in terms of a single trig function.

ii) Find all values of x in the interval 0<x<360 for which sin2x+cos(90-2x) = -1

2) Find the least positive value of angle A for which sin A = 0.2 and cos A is negative.

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The first one I'm not sure how to do it now that they're are both sin and cos involved :confused:

Second one, I'm not sure how to go about doing it.

(edited 13 years ago)

Reply 1

nuodai

17

For Q1 have you tried using the angle-addition formula for

\cos(A+B)

? Then you use your answer to do part (ii).

For Q2, I assume you mean "least positive" rather than "least possible"? You'll find that there are infinitely many values of

A>0

for which

\sin A = 0.2

, but for some of these,

\cos A

will be positive, and for the others it will be negative. You need to find the first one such that

\cos A<0

.

RIP

OP

1)I dont think I've done that angle addition formula thing yet .

2) I'll try doing it soon.

Reply 4

WildBerry

OP

Original post by Rahul.S

RIP

Reply 5

Thrug

3

What exam board are you on WildBerry?

I'm on edexcel and haven't come across any questions like these.

Reply 6

WildBerry

OP

Original post by Thrug

What exam board are you on WildBerry?

I'm on edexcel and haven't come across any questions like these.

I'm on OCR, they're from the Misc exercise of their textbook, the topics are usually harder than normal questions .

Reply 7

xPixie

Wow.. My C2 wasn't as hard as this :s-smilie:

Reply 8

nuodai

17

Original post by WildBerry

1)I dont think I've done that angle addition formula thing yet .

2) I'll try doing it soon.

Thinking about it, angle-addition formulae don't come up until C3. In that case, draw a graph of

y=\cos (90-2x)

and

y=\sin 2x

on the same axes, and work out what graph transformations are necessary to turn the sine graph into the cosine graph. Then using your C1 knowledge of graph transformations, you'll be able to write

\cos (90-2x)

in terms of

\sin 2x

.

Reply 9

WildBerry

OP

Original post by xPixie

Wow.. My C2 wasn't as hard as this :s-smilie:

I've been told to do around 15 questions like these

I've done 10, but there are around 5 more really hard ones that I just dont know how to start. I'll probably just do what I can after doing these, and get the usual C grade written on for not attempting the rest, even though the crap teacher hasn't taught any of this yet. :rolleyes:

Reply 10

xPixie

Original post by WildBerry

I've been told to do around 15 questions like these

I've done 10, but there are around 5 more really hard ones that I just dont know how to start. I'll probably just do what I can after doing these, and get the usual C grade written on for not attempting the rest, even though the crap teacher hasn't taught any of this yet. :rolleyes:

Q1i sounds like a C4 question & I've just started that now :s-smilie:

What board are you? Because I'm on OCR MEI, and their papers aren't as hard as this. If you want to revise, just do past papers, that's the best way to revise maths :smile:

Reply 11

WildBerry

OP

Original post by xPixie

Q1i sounds like a C4 question & I've just started that now :s-smilie:

What board are you? Because I'm on OCR MEI, and their papers aren't as hard as this. If you want to revise, just do past papers, that's the best way to revise maths :smile: