A right angled triangle with 2 angles, a and b.
If a < b, how many answers will the following give?
sina x sinb
sina x cosb
cosa x sinb
cosa x cosb
Answers are:
A- 1
B- 2
C- 3
D- 4
E- depends on the value of a
2006-11-09 23:01:50 · 8 answers · asked by Robert A 3 in Science & Mathematics ➔ Mathematics
C - 3 possible answers
In any given right triangles with the two other angles being a and b,
sin a = cos b AND sin b = cos a,
as such, the first and fourth combination will give one answer, the other two will either give square trigonometric values of each angle i.e. sin^2 a and cos^2 a OR sin^2 b and cos^2 b.
The only condition that will not satisfy this is when the angle is 45 degrees, which means a = b and contradicting the given statement of a being less than b.
Thus the answer is C.
2006-11-11 06:07:29 · answer #1 · answered by alistair_uk 2 · 0⤊ 0⤋
Consider the following right angled triangle
a
--|\
A| \ H
--|__\b
---B
a, b are the two, non right angled, angles
A, B and H are the three sides of the triangle
the formula for sin is opposite / hypotenuse
the formula for cos is adjacent / hypotenuse.
Therefore
sina = B/H
cosa = A/H
sinb = A/H
cosb = B/H
Therefore sina = cosb and cosa = sinb!
So
sina x sinb = sina x cosa = AB/H^2
sina x cosb = sina x sina = B^2/H^2
cosa x sinb = cosa x cosa = A^2/H^2
cosa x cosb = cosa x sina = AB/H^2
Therefore there are only three answers so far.
Since you know a < b the length of the sides B and A are different. In fact B < A.Therefore the above three results are all unique so it doesn't depend on the value of a.
If this condition a < b didn't exist then the answer would depend on the value of a since a could be 45 degrees which would make b 45 degrees and so sina = cosa = sinb = cosb making there be only one answer. But this isn't the case
Answer : 3 different answers - C
2006-11-10 09:06:45 · answer #2 · answered by Steve G 2 · 1⤊ 1⤋
Have problems with Mathematics? study hard, learn smart and use tools
http://www.goldenmouse.net/Mathematics.html
Try "Solving Triangles"
The program provides detailed, step-by-step solutions in a tutorial-like format to the problems of solving triangles in elementary geometry. The program is designed for high school students and teachers.
2006-11-10 07:38:17 · answer #3 · answered by Allen 2 · 0⤊ 2⤋
E since sin a could = cos b
2006-11-10 08:19:13 · answer #4 · answered by dragongml 3 · 0⤊ 1⤋
because sin(a) * cos(b) = cos(a) * sin(b), and because a < b is a strict inequality (eliminating a = b), the answer is c; there are 3 different answers.
2006-11-10 11:39:40 · answer #5 · answered by michaell 6 · 0⤊ 0⤋
They will depend on the value of a. ie. (E)
like for the first one sin(a)*sin(b) = sin(a)*sin(90-a) = sin(a)*cos(a)
2006-11-10 07:35:59 · answer #6 · answered by Anonymous · 0⤊ 2⤋
Someone struggling with their homework again?!?
We didn't have this when I were a lad, had to work it out ourselves etc. etc. etc......
2006-11-10 07:23:35 · answer #7 · answered by Ecko 4 · 0⤊ 2⤋
get a life bob u plonker
2006-11-10 07:05:04 · answer #8 · answered by del 4 · 2⤊ 3⤋