What is the answer to this?
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
Answers:
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.
get a life bob u plonker
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..
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)
Have problems with Mathematics? study hard, learn smart and use tools
http://www.goldenmouse.net/mathematics.h.
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.
E since sin a could = cos b
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
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.
are all cells the same?
How Hereditary Is Red Hair?
Why do frogs leave their ponds and go walkabout in the Spring?
what is the closest relative to the dinosaurs this days?
Find all of the solutions of the equation?
Ok if we know space is 13.7 billion years old. What day is its birthday?
Why do zebras have stripes?
Putting a nuclear bomb in a box?
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
Answers:
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.
get a life bob u plonker
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..
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)
Have problems with Mathematics? study hard, learn smart and use tools
http://www.goldenmouse.net/mathematics.h.
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.
E since sin a could = cos b
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
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.
The answers post by the user, for information only, UKQnA.com does not guarantee the right.