Question

tan a = 24/7 and a is in QIII. What is cos(a – pi)?

7/25
-7/25
-24/7
24/7

Answer 1

Is this correct?
invtan(24/7)= 1.2870022175865687736056184574346. This is in quarter I so I add pie to it, but then subtract it in cos(a-pi). I then cosine it to get .28, or 7/25.

Did i do it correctly?

Answer 2

Lets start with process of elimination first then start solving should we

Answer 3

you in q3 tangent is positive right?

Answer 4

draw a triangle

find x using pythagoras

Answer 5

next find sin(a) and cos(a) after finding x
then use
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Answer 6

Magnitude is 25

Answer 7

that will give you the value of
cos(a - pi)

Answer 8

You gave me a sum and difference identity, i do not see an A or B

Answer 9

Ahh

Answer 10

you use the identity... let A = a and B = pi

does that make sense

Answer 11

-cos(a)

Answer 12

and you should know what

\[\cos(\pi) = ?.... and..... \sin(\pi) = \]

Answer 13

oops the substitution should be
\[\cos(a - \pi) = \cos(a)\cos(\pi) + \sin(a)\sin(\pi)\]

Answer 14

cos(pi)=-1
sin(pi)=0
so it should reduce to what i just said of -cos(a) right?

Answer 15

ok... from the triangle in the 3rd quadrant, what is the value of cos(a)..?

Answer 16

that's correct... but you need to find cos(a) in this quadrant...

Answer 17

-0.28=cos(a)

Answer 18

if you look at the triangle are you happy that cos(a) = -7/25 sin(a) = -24/25

Answer 19

im happy? ok lol
yep

Answer 20

\[\cos(a - \pi) = \cos(a)\cos(\pi) + \sin(a)\sin(\pi)\]

which is

\[\cos(a - \pi) = \frac{-7}{25} \times - 1 + \frac{-24}{25} \times 0\]

which will give you an answer... from your list of choices

Answer 21

which gives me 7/24
im sure theres a reason but why is doing it like that better than
cos((invtan(24/7)+pi)= 7/24

Answer 22

because, looking at how you managed you're solution, it wasn't an exact value. The question gave answer choices that are exact values....

for me the question is asking you to use your trigonometry skills. Show what you know. my method shows a lot of understanding...

Answer 23

ok