Trig question 2 unit prelim (2 Viewers)

[girlworld_club]

simplify sin(360-x) x tan(90-x)

Please show full working.

 

[Timske]

I'm guessing you're stuck at tan(90-x) amirite?

 

[girlworld_club]

all of it

 

[SpiralFlex]

 

[girlworld_club]

How did you get the first line of working?

 

[Carrotsticks]

simplify sin(360-x) x tan(90-x)

Please show full working.

sin(360-x) = -sin(x)

tan(90-x) = cot(x)

so therefore answer is cot(x) x -sin(x) = -cos(x).

 

[SpiralFlex]

Sine is negative in the 4th quadrant.

 

[girlworld_club]

again..
how did you get this?

sin(360-x) = -sin(x)

tan(90-x) = cot(x)

 

[girlworld_club]

why did sine stay as sine, however tan changes to cot

 

[Carrotsticks]

When dealing with complementary angles ie: 90 degrees, the actual function usually changes.

ie: sin(90-x) = cos(x)

When dealing with a more 'supplementary-type angle' ie: 180 and 360 degrees, the function doesn't change but the sign does.

 

[Drongoski]

sin(360 - x) = sin(360 - x -360) = sin (-x) = -sin x

 

[girlworld_club]

according to you then sine should not change ??? for 360

 

[Carrotsticks]

according to you then sine should not change ??? for 360

It didn't.

sin(360-x) was still a sine function afterwards.

However instead of a + sign in front, it's now a minus.

 

[Bozza555]

All Stations To Central breh

 

[RivalryofTroll]

again..
how did you get this?

sin(360-x) = -sin(x)

tan(90-x) = cot(x)

If you follow the ASTC rule,
Sin is negative in the 3rd and 4th quadrants where it's 180 + x and 360 - x.
Sin is positive in the 1st and 2nd quadrants where it's 180 - x and x.

Therefore, sin(360-x) = -sin(x)

tan(90-x) = cot(x) is an identity for complementary angles.

You can find the proof for it in your Mathematics textbook.

 

[Timske]

You can do the + and - method but that's tedious

 

[girlworld_club]

hmm..still confused why tan(90-x) turned into cot(x) and not tan(x).

 

[fishrushed]

tan(90-x)=cot(x) is an identity or a rule, just like sin(90-x)=cos(x)
Its just one of those things you have to remember.

 

[Drongoski]

according to you then sine should not change ??? for 360

You can add or subtract 360 degrees any number of times and it would make no difference to the sin, cos or tan of an angle.

e,g. sin(37) = sin(37 + 360) = sin(37 + 6x360) = sin(37-77*360)

tan(19) = tan(19+720) = tan(19-5*360) = tan(19-7053*360)

Try the various cases on your calculator and satisfy yourself it's true.

 

[girlworld_club]

if sin =
sin (90-x) = cos (x)

then why does sin (360-x) = -sinx