trig equation help!!! 2014 hsc mcq (1 Viewer)

[jojosiwa123]

hey guys, could someone please help me with this question... yes I know I should be able to answer it by now but maths is my worst subject so don’t bully me pls

theres 2 solutions (from tan) but I genuinely don’t get how to find them... and I don’t get why pi/2 can’t be a solution?

thanks!!

 

[Haruto_65]

http://www.projectmaths.com.au/assets/M-2014-7.pdf

 

[jojosiwa123]

http://www.projectmaths.com.au/assets/M-2014-7.pdf

ive seen that but how do I know tan has 2 solutions?

 

[erucibon]

ive seen that but how do I know tan has 2 solutions?

Put tan^-1(2) into calc and you get around 63 degrees. As it is -2, solutions are in quadrants 2,4, so take 180-63 and 360-63

 

[Haruto_65]

ive seen that but how do I know tan has 2 solutions?

The question is exactly like a quadratic.
(sinx-1)(tanx-2)=0
where sinx = 1
tanx = -2

sinx= 1 has one solution (as there is only 1 spot in the domain where sin equals positive one) which is 90 degrees.
Similarly tanx = -2 has two solutions which lie within quadrants 2 and 4 (to find it you can do tan inverse on you calculator)

However since the equation is like a quadratic, when you insert all the solutions it should equal zero. But since tan90 is undefined it does not satisfy the equation, hence only 2 solutions overall.

 

[beetree1]

hi jojosiwa u got this

 

[jojosiwa123]

Put tan^-1(2) into calc and you get around 63 degrees. As it is -2, solutions are in quadrants 2,4, so take 180-63 and 360-63

The question is exactly like a quadratic.
(sinx-1)(tanx-2)=0
where sinx = 1
tanx = -2

sinx= 1 has one solution (as there is only 1 spot in the domain where sin equals positive one) which is 90 degrees.
Similarly tanx = -2 has two solutions which lie within quadrants 2 and 4 (to find it you can do tan inverse on you calculator)

However since the equation is like a quadratic, when you insert all the solutions it should equal zero. But since tan90 is undefined it does not satisfy the equation, hence only 2 solutions overall.

thank you both so so much!!

 

[cossine]

As Haruto mention tan pi/2 is undefined. This because of the definition.

The definitions of trigonometric function from the unit circle are:

tan theta = y/x (At pi/2, y = 1, x=0 therefore tan(pi/2) = 1/0 )

cos theta = x

sin theta = y