Trigonometry (1 Viewer)

[skillstriker]

How do you simplify:

1) sin(270-theta)
2) cos(90+theta)
3) tan(theta-180)

Full working please. Thank You!

 

[bleakarcher]

Use the double angle formulae..
Fairly standard mate.

1) sin(270-a)=sin(270)cos(a)-sin(a)cos(270)=-sin(90)cos(a)-cos(90)sin(a)=-cos(a)

By similar process:

2) cos(90+a)=-sin(a)

3) tan(a-180)=tan(a)

These results are also quite obvious after observing the unit circle.

 

[Timske]

1) sin(270-theta) = sin270costheta - cos270sintheta = -costheta
2) cos(90+theta) = cos90costheta - sin90sintheta = -sintheta
3) tan(theta-180) = tantheta - tan180 / 1 + tanthetatan180 = tantheta

 

[nightweaver066]

1. sin(270 - theta)
= sin(180 + 90 - theta)
= -sin(90 - theta)
= -costheta

2. cos(90 + theta)
= cos(180 - (90 - theta) )
= -cos(90 - theta)
= -sintheta

3. tan(theta - 180)
= tan(-(180 - theta))
= -tan(180 - theta)
= tantheta

 

[skillstriker]

Thanks. I haven't learnt the double angle formula yet. So with these questions do you just have to force them into (90-theta), (180-theta), (180+theta), (360-theta)?

 

[nightweaver066]

I suppose so, but it's better to understand them.

E.g. For the first question, sin(270 - theta), i know that this would result in it's complementary angle as it's not starting from 180.
The result will also be negative as it's in the 3rd quadrant so it would equal to -costheta.

You can easily apply similar logic to the other questions and get the answers.