Question

Find the exact value of the expression.

Answer 1

I got -0.866, how to I get that into a fraction?

Answer 2

Step 1: Put down your calculator. :)

Answer 3

Step 2: recall the identity: sinxcosy-cosxsiny= what??

Answer 4

I don't know.

Answer 5

Well, review the trig identities because apparently you are supposed to know them. :)

sinxcosy-cosxsiny= sin(x-y)

Answer 6

So now can you simplify the expression in the problem?

=??

Answer 7

I don't think so.

Answer 8

Just use the identity, letting x=265*, y=25*

Then it =sin(265-25)=sin240*

Answer 9

Now sin(240*) should be one that you know exactly - it has a reference angle of ___ and is in quadrant ___ so the sine is (positive or negative)?

Answer 10

Negative

Answer 11

yes, good, it's negative. and it's value is the same as sin(60) (since that's the reference angle), EXCEPT FOR the sign (which we've determined is negative.

That is:
sin(240*)=-sin(60*)

Answer 12

so now you just need to know the sin(60*). Do you know the common angle function values? In the first quadrant, the easiest way is using SOHCAHTOA and a 30-60-90 triangle, but you may have learned them differently.

Answer 13

I think I figured it out. I got A

Answer 14

Is sin(60)=1/2???

Answer 15

is -1/2 = what you got on your calculator? :)

Answer 16

Wolfram

Answer 17

Check again.

Answer 18

But truly, I'm sure you are expected to know the function values for multiples of 30, 45 and 60 without a calculator. They are the basic building blocks.

Answer 19

Wasn't taught them :(