more trig

william · #1 $Old$ December 14th, 2008, 10:08 AM

1. show that cos150/sin150=1/tan150

2. prove tan O cos O = sin O

Chris L T521 · #2 $Old$ December 14th, 2008, 10:10 AM

Quote:

Originally Posted by william $View Post$

1. show that cos150/sin150=1/tan150

2. prove tan O cos O = sin O

Hint: $\cot\vartheta=\frac{\cos\vartheta}{\sin\vartheta}$ and $\tan\vartheta=\frac{\sin\vartheta}{\cos\vartheta}$ .

Do you think you can do these now?

william · #3 $Old$ December 14th, 2008, 10:48 AM

Quote:

Originally Posted by Chris L T521 $View Post$

Hint: $\cot\vartheta=\frac{\cos\vartheta}{\sin\vartheta}$ and $\tan\vartheta=\frac{\sin\vartheta}{\cos\vartheta}$ .

Do you think you can do these now?

can you be a bit more specific i am not sure exactly what you mean

euclid2 · #4 $Old$ December 14th, 2008, 11:11 AM

Quote:

Originally Posted by william $View Post$

1. show that cos150/sin150=1/tan150

2. prove tan O cos O = sin O

2.
Prove that $tan\vartheta cos\vartheta = sin \vartheta$

$=tan\vartheta cos\vartheta = sin \vartheta$

$=(sin\vartheta/cos\vartheta)cos\vartheta$

$=sin \vartheta$

tester85 · #5 $Old$ December 14th, 2008, 11:17 AM

Being more specific is like providing the answer for this particular question but nevertheless hope you will be able to learn from the answer and solve future proving problems.

tan O cos O = sin O

From L.H.S
(sin O/cos O) cos O
sin O (proven)

Quote:

Originally Posted by william $View Post$

can you be a bit more specific i am not sure exactly what you mean

tester85 · #6 $Old$ December 14th, 2008, 11:25 AM

For the first question,

cos150/sin150=1/tan150

From R.H.S

1/tan150 = ( 1/sin150/cos150 )
1/sin150/cos150 = 1 x cos150/sin150
= cos150/sin150 (proven)

For proving question try to have a formula sheet which contains all the trigo identities and ask yourself a few qns like what trigo identity can i use to solve the problem. You will be able to solve problem fairly easily with constant practice. Hope it helps.

euclid2 · #7 $Old$ December 14th, 2008, 11:32 AM

Quote:

Originally Posted by william $View Post$

1. show that cos150/sin150=1/tan150

2. prove tan O cos O = sin O

1. cos150/sin150=1/tan150

sketch the angle in standard position. Then determine the values of x,y,r,using the 30 deg triangle and that it lies in the quadrant 2.

from the diagram, i can see that
1.cos150=-sqrt3/2
2.sin150=1/2
3.tan150=-1/sqrt3

therefore: cos150/sin150=1/tan150
=-sqrt3/2over1/2 = 1/1/-sqrt3
=(-sqrt3/2)(2/1)=1*-sqrt3/1
=-sqrt3=-sqrt3

therefore: cos150/sin150=1/tan150