Question

Use identities (no calculators) to find the exact value for (sin 9)(sin 36)-(cos 9)(cos 36)

Answer 1

9+36 =?

Answer 2

how can you play with those angles to get an angle for which there is an exact value

Answer 3

does this equals cos 45?

Answer 4

yes

Answer 5

which is 1/ sqrt(2)

Answer 6

\[\sin \theta = \cos 90 - \theta\]

Answer 7

How do I figure out if its positive of negative

Answer 8

sines, cosines and tangents in the first quadrant (0-90 degrees) are all positive

Answer 9

i've just checked my maths formula book and the given expression = -cos(9 + 36) not
cos (9+36) so the correct answer is -(1/sqrt2)

Answer 10

this is not the formula for \[cos(a+b)\] but it is its negative.

Answer 11

of course 9+36=36+9=45

Answer 12

but the formula for
\[cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\]

Answer 13

and \[sin(a)sin(b)-cos(a)cos(b)=-(cos(a)cos(b)-sin(a)sin(b)\] that is why you had to change the sign from
\[\frac{\sqrt{2}}{2}\]to
\[-\frac{\sqrt{2}}{2}\]