Additional Maths: Trigonometric Fnc

Nathpoop SG

How do i solve the following questions?

Find the values of θ, where θ is more than or equal to 0deg and less than or equal to 360deg

1(a)

(sin θ - 1)(sin θ +1) = 0

Ans: 90deg, 270deg

(b)

sin θ (2 cos θ - 3) = 0

Ans: 0deg, 180deg, 360deg.

Thanks in advance! (:

Mikethm SG

sin^2 x -1 = 0

sin^2 x = 1

sin x = +/-1

Reference angle = 90

x = 90 or 270.

sin x(2cos x -3) = 0

sin x = 0 or cos x = 3/2 (NA)

Reference angle = 0

x = 0, 180 or 360.

Sec 3 not Sec 4 right?

SBS n SMRT SG

Yes, trigo is in sec 3

jayh272416 SG

sin^2 x -1 = 0

sin^2 x = 1

sin x = +/-1

Reference angle = 90

x = 90 or 270.

you can simply jump to sin x = +/-1 lol. since its already statede (sin x +1) (sin x -1) = 0 lol

SBS n SMRT SG

you can simply jump to sin x = +/-1 lol. since its already statede (sin x +1) (sin x -1) = 0 lol

no lah

(sinx+1)(sinx-1)=o

sinx+1 = 0 or sinx-1=0

sinx=+/- 1

this way of presenting is clearer

wee_ws SG

Hi Nathpoop,

Schools like to set questions like

(sin θ - 1)(sin θ + 1) = -1/2,

so be sure to know how to tackle these too. Thanks!

Cheers,
Wen Shih

Nathpoop SG

I don't get it why is the answer for part(b) 0deg, 180deg, 360deg. Like the ASTC which quadrant they are in? And how do i arrive to the answer from the reference angle, 0 deg?

Mikethm SG

you can simply jump to sin x = +/-1 lol. since its already statede (sin x +1) (sin x -1) = 0 lol

Thank you but my way is less time consuming than writing "sinx =1 or sinx = -1" and clearer than jumping straight to "sinx =+/-1". Lumping it together allow me to do with one SATC diagram instead of 2.

To Nathpoop:

Follow the arrows in calculating.

Nathpoop SG

Total there are for quads

0deg in 1st quad

180 in 2nd quad

360 in 4th quad

am i correct?

If i refer to your diagram wouldn't it be 4 answers instead of 3?

x = 0, 180 - 0, 180 + 0, 360 - 0

= 0, 180, 180, 360

therefore x = 0, 180, 360.

Am i right to show this as my working?

Mikethm SG

Total there are for quads

0deg in 1st quad

180 in 2nd quad

360 in 4th quad

am i correct?

If i refer to your diagram wouldn't it be 4 answers instead of 3?

x = 0, 180 - 0, 180 + 0, 360 - 0

= 0, 180, 180, 360

therefore x = 0, 180, 360.

Am i right to show this as my working?

Depend on what you would show for say... (x-2)(x-2)=0

Personally I would just show "x=2" instead of "x=2 or x=2"

Nothing wrong with showing repeated roots but would annoy some. So I wouldn't.