trig qn. (1 Viewer)

[jannny]

Simplify (I'll use @ for theta)

(sin @) sin( 180 - @) - sin(90 - @) cos(180 - @)

the final answer is 1.

and with the solutions how did

sin (180 - @) = sin @?
sin ( 90 - @) = cos @ ?
cos ( 180 - @) = - cos @?

thanks, cheers.

 

[Forbidden.]

Simplify (I'll use @ for theta)

(sin @) sin( 180 - @) - sin(90 - @) cos(180 - @)

the final answer is 1.

and with the solutions how did

sin (180 - @) = sin @?
sin ( 90 - @) = cos @ ?
cos ( 180 - @) = - cos @?

thanks, cheers.

sin (180 - θ) = sin θ
&
cos (180 - θ) = - cos θ

You know the four quadrants ASTC ?
1st. quad: All trig ratios are positive (θ)
2nd. quad: Sin only is positive (180 - θ)
3rd. quad: Tan only is positive (180 + θ)
4th. quad: Cos only is positive (360 - θ)

E.g
If θ were 45⁰

cos 45⁰ (1st quadrant; All trig ratios are positive)

cos 135⁰ = cos (180⁰ - 45⁰) =
- cos 45⁰ (2nd quadrant; cos is negative)

cos 225⁰ = cos (180⁰ + 45⁰) =
- cos 45 (3rd quadrant; cos is negative)

cos 315⁰ = cos (360⁰ - 45⁰) =
cos 45⁰ (4th quadrant; cos is positive)


sin ( 90⁰ - θ) = cos θ

The best way I can explain is:

sin 90 = cos 0 (cos 0 = 1 & sin 90 = 1)
sin 30 = cos 60 (cos 60 = 0.5 & sin 30 = 0.5)

It's from the Preliminary Maths course.

Remember:

sin ( 90⁰ - θ) = cos θ
cos ( 90⁰ - θ) = sin θ
tan ( 90⁰ - θ) = cot θ
sec ( 90⁰ - θ) = cosec θ
cosec ( 90⁰ - θ) = sec θ
cot ( 90⁰ - θ) = tan θ

 

[jannny]

alright got it. ta =]