C2: Trig

Please help:

Given that angle B is reflex and tan B = + (?21)/2, find the exact value of:

(a) sin B

(b) cos B

Actual solution to (a) - (?21)/5, (b) - 2/5

Please guide me through every step to solve this question.

Thanks

Reply 1

Christophicus

18

blah888

Please help:

Given that angle B is reflex and tan B = + (?21)/2, find the exact value of:

(a) sin B

(b) cos B

Actual solution to (a) - (?21)/5, (b) - 2/5

Please guide me through every step to solve this question.

Thanks

I'll assume the ? represents √
If angle B is reflex it lies in quadrant 3 (180-270°)
In quadrant 3, tanB is +ve, cosB is -ve and sinB is -ve.
Draw a right angled triangle. Label one of the angles B, write opp = √21 and write adj = 2. Simple pythagoras theorem shows you that, hyp = √25 = 5.

a) sin B = opp/hyp = -√21/5 (since sin B is -ve)
b) cos B = adj/hyp = -2/5 (since cos B is -ve)

Reply 2

Jonny W

8

tan(B) = sqrt(21)/2

We are told that B is reflex: ie, that 180 <= B <= 360.

But since tan(B) > 0, we can say more: 180 <= B <= 270.

cosec^2(B) = 1 + cot^2(B) = 1 + 4/21 = 25/21
cosec(B) = -5/sqrt(21) . . . . . negative root because 180 <= B <= 360
sin(B) = -sqrt(21)/5

sec^2(B) = 1 + tan^2(B) = 1 + 21/4 = 25/4
sec(B) = -5/2 . . . . . negative root because 180 <= B <= 270
cos(B) = -2/5

Reply 3

Eau

OP

15

Thanks for the concise response. And yeah "?" represents root. How come my roots comes out funny and yours doesn't?

Reply 4

Eau

OP

15

Jonny W, thanks for your part, but I haven't learnt cosec, sec ... yet, so i have no idea what you said.

Reply 5

Eau

OP

15

I always want to give you guys rep, but for some reason, I am always out of them.

Reply 6

goku999

3

you will learn the cosec, cotan and sec in C3 but i dont remember it being in C2 unless its to do with the identities

Reply 7

goku999

3

blah888

I always want to give you guys rep, but for some reason, I am always out of them.

you can only rep once every 24 hours

Reply 8

Eau

OP

15

goku999

you can only rep once every 24 hours

yeah i know that, thanks for reminder :frown:

Reply 9

Arminius

14

cosecx is 1/sinx

Yer, you learn it in A2 ( we were told to learn our trig over the summer last year).

Reply 10

Eau

OP

15

Zakatu

cosecx is 1/sinx

Yer, you learn it in A2 ( we were told to learn our trig over the summer last year).

I see, so cosecx is like the inverse of sinx.

So then is cosecx the same as sin^-1 x? Prob not, just asking.

But why called cosec? can't it be like insin or whatever?

Reply 11

Christophicus

18

blah888

I see, so cosecx is like the inverse of sinx.

So then is cosecx the same as sin^-1 x? Prob not, just asking.

But why called cosec? can't it be like insin or whatever?

don't get confused.
cosecx = 1/sinx = (sinx)^-1
arcsinx = sin^-1x (don't worry about this, it is different from cosecx and you will learn about inverse functions in C3)

Reply 12

goku999

3

Somethings in maths are called what they are.
Kind of confusing as the past great mathematicians call their discoveries a variety of names.

also:

secx=1/cosx
cotanx=1/tanx

If u want to know about this do A-Level maths, its fun

Reply 13

Eau

OP

15

goku999

Somethings in maths are called what they are.
Kind of confusing as the past great mathematicians call their discoveries a variety of names.

also:

secx=1/cosx
cotanx=1/tanx

If u want to know about this do A-Level maths, its fun

Yeah, i know maths is fun. That's why I'm doing Further Maths too! :biggrin:

C2: Trig

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