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URGENT Math trig help!

I have my SAT subject test tomorrow so it's urgent!

If 90° < a < 180° and 270° < b < 360°, then which of the following cannot be true?

(A) sin a = sin b
(B) tan a = sin b
(C) tan a = tan b

The answer given is (A) and I agree that it is correct as 'cannot be true'.

However even (B) 'cannot be true' because the graphs of (tan a) and (sin b) intersect only at multiples of 180, none of which are used in the domains given so this question has two answers, (A) and (B)...

Do you think my logic is correct?
Original post by BamboozlingDance
I have my SAT subject test tomorrow so it's urgent!

If 90° < a < 180° and 270° < b < 360°, then which of the following cannot be true?

(A) sin a = sin b
(B) tan a = sin b
(C) tan a = tan b

The answer given is (A) and I agree that it is correct as 'cannot be true'.

However even (B) 'cannot be true' because the graphs of (tan a) and (sin b) intersect only at multiples of 180, none of which are used in the domains given so this question has two answers, (A) and (B)...

Do you think my logic is correct?


Nope.

You are assuming that a=b when you're doing your comparision, and that is not the case.

E.g. Let a=153.4349... and b= 330

Then tan a = -0.5 = sin b.

So (B) can be true.

(A) can never be true, because sin a is positive in the given quadrant for a, and sin b is negative in the given quadrant for b, and hence they cannot be equal.
(edited 10 years ago)
Oh yes! How dumb of me!
Thanks!
Original post by BamboozlingDance
I have my SAT subject test tomorrow so it's urgent!

If 90° < a < 180° and 270° < b < 360°, then which of the following cannot be true?

(A) sin a = sin b
(B) tan a = sin b
(C) tan a = tan b

The answer given is (A) and I agree that it is correct as 'cannot be true'.

However even (B) 'cannot be true' because the graphs of (tan a) and (sin b) intersect only at multiples of 180, none of which are used in the domains given so this question has two answers, (A) and (B)...

Do you think my logic is correct?


NO. tana<0 in second quadrant and sinb<0 in fourth so B can be true

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