Geometry example ptoblems

GEOMETRY:

QUESTION : 15

 

If cos teta = ¾ and is in the fourth quadrant, find sin teta.

 

 

Solution:

 

Using pythagoras theorem,

 

3^2 + y^2 = 4^2

 

9 + y^2 = 16

 

y^2 = 16 - 9

 

y = +/- root of 7

 

Here,

 

y lies in the fourth quadrant so, it takes the value -ve root 7.

 

Sin teta = root 7/4.

 

 

 

GEOMETRY

QUESTION: 16:

 

Find Tan (75) using sum or difference angle method.

 

Solution:

 

Tan 75 = tan (45 + 30)

 

tan x + tany

tan(x+y ) = ---------------

1- tanx. Tany

 

Using the above method

 

Tan 45 + tan 30

Tan(45+30) = ----------------------

1- tan45. tan 30

 

1+ 1/ 3

= ------------------

1- 1. 1/ 3

 

 

 

 

 

 

 

 

 

GEOMETRY:

QUESTION : 17:

 

Find sin 75 using sum or difference of angle method.

 

 

Solution:

 

Sin 75 = sin (45 + 30)

 

Sin (x+ y) = sinx cosy + cosx siny.

 

Sin(45 + 30) = sin 45 cos 30 + cos 45 sin 30.