Question

what does cos 200=cos? is sin200=-sin20

Answer 1

umm , repeat?

Answer 2

Angles have the same trig function values if:
- they have the same reference angle (angle between the terminal side of the angle and the x-axis
AND
- they are in quadrants where that trig function has the same sign.

Answer 3

So for sin200 and sin(-20):

Answer 4

Are the reference angles the same?

Does the sine function have the same sign, in each case?

Answer 5

oohhhhhh

Answer 6

See what I mean? :)

Answer 7

so its just asking for the coteminal angle ok
Thanks!

Answer 8

NO, this is different than coterminal!

Answer 9

Coterminal angles are separated by 360*. They also have the same function values - always. But this is different.

Answer 10

For every angle in Q1, there is an angle in Q2 that has the same sine value. Since sine>0 in both Q1 and Q2, the angles with the same reference angles have exactly the same sine value.

E.g.:

sin(80*)=sin(100*) ---> they have the same reference angle, and both has positive sine.

They are NOT coterminal.

That's what this problem is getting at.

Answer 11

oh. well is it the same thing with cos?

Answer 12

So 200* and -20* are in Q3 and Q4, both have negative sine values. And they have the same reference angle. SO... their SINE values are equal.

Now apply that same analysis to find the angle that has cosine value = cos(200*)

Answer 13

It's the same ANALYSIS, but WHERE does cosine have the same sign, as what it has in Q3?

Answer 14

E.g., what quadrant will you be in, to find an angle that has the same cosine as 200*?

Answer 15

4

Answer 16

What sign does cosine have in Q3?

What sign does it have in Q4?

Answer 17

-in 3 + in 4

Answer 18

Right. So it's NOT 4.

Try again: what quadrant will you be in, to find an angle that has the same cosine as 200*?

Answer 19

Besides Q3, what quadrant also has negative cosine values?

Answer 20

quad 2

Answer 21

RIGHT! so you need an angle in Q2, such that it has the same reference angle as 200*

Answer 22

Do you understand what I mean by reference angle? What is the ref angle of 200*?

Answer 23

split 200 in n(pi) + x .. after that check on the value whether the cos is +ive or -ive then answer would be +-cos x

Answer 24

cos(160) then?

Answer 25

Exactly!! :)

Answer 26

thanks so much that helped alot!