Okay, I have solved this many times and I am getting a different answer from the teacher key.
Given cosA = 4/5 and tanB = 5/12 with both angles in quadrant one, find the exact value of the given function.
14) sin(A-B)
15) sec(A+B)
16) cot(B-A)
So! Here is how I started solving....
given the cosA = 4/5 I found the triangle values, 5 hypotenuse, 4 Adjacent, 4 Opposite
given the tanB = 5/12; the hypotenuse is 13, 12 adjacent, 5 opposite...Right? They should be Pythagorean triples.
By taking that, for #14 I plugged in
sin ((3/5) - (5/13))
which led me to
sin((39/65) - (25/13)) = sin(14/65)
Is that not the answer? The key says: 16/65. Did I make a mistake?
Now for #15 sec(A+B)
take them same numbers and shouldn't it be sec((5/4) + (13/12))?
by reducing that I get: 7/3 but the answer key says 65/33 what did I do wrong? Isn't cos = Adjacent / Hypotenuse making sec = Hypotenuse / Adjacent
for #16 cot(B-A)
((12/5) - (4/3)) simplified to
(16/15) while the key says -63/16
Thank you so much for help, sorry if my formatting is bad. //edit: formatting
Given cosA = 4/5 and tanB = 5/12 with both angles in quadrant one, find the exact value of the given function.
14) sin(A-B)
15) sec(A+B)
16) cot(B-A)
So! Here is how I started solving....
given the cosA = 4/5 I found the triangle values, 5 hypotenuse, 4 Adjacent, 4 Opposite
given the tanB = 5/12; the hypotenuse is 13, 12 adjacent, 5 opposite...Right? They should be Pythagorean triples.
By taking that, for #14 I plugged in
sin ((3/5) - (5/13))
which led me to
sin((39/65) - (25/13)) = sin(14/65)
Is that not the answer? The key says: 16/65. Did I make a mistake?
Now for #15 sec(A+B)
take them same numbers and shouldn't it be sec((5/4) + (13/12))?
by reducing that I get: 7/3 but the answer key says 65/33 what did I do wrong? Isn't cos = Adjacent / Hypotenuse making sec = Hypotenuse / Adjacent
for #16 cot(B-A)
((12/5) - (4/3)) simplified to
(16/15) while the key says -63/16
Thank you so much for help, sorry if my formatting is bad. //edit: formatting