trigonometry

3. ■ Trigonometry (fromGreek trigōnon,
"triangle" and metron, "measure") is a branch
of mathematics that studies relationships
involving lengths and angles of triangles.The
field emerged during the 3rd century BC from
applications of geometry to astronomical
studies.

7. ■ Basic identities:-

9. Q) tan x sin x + cos x = sec x
Solution:We will only use the fact that sin² x +
cos² x = 1 for all values of x.
LHS = tan x sin x + cos x
=>sin x/cos x. sin x +cosx
= >sin² x/ cos x + cos x
=>sin² x/ cos x + cos²x /cosx
=> sin² x + cos² x/ cos x
= >1/ cos x = RHS

11. Q) Cos² 20+cos² 70/sin² 31+sin² 59+sin²
64+cos64.sin26
Solution:- cos² 20+sin² (90-70)/sin² 31+sin² (90-
59)+sin² 64+cos64.cos64
=> 1+sin² 64+cos² 64
=>1+1
=>2

12. A PPLICATIONS OF
TRIGONOMETRY

13. ■ We observe generally that children usually
look up to see an airplane when it passes
overhead.This line joining their eye to the
plane while looking up is called LINE OF
SIGHT.

14. ■ The angle which the line of sight makes with a
horizontal line drawn away from their eyes is
called the ANGLE OF ELEVATION of airplane
from them.

15. ■ If the pilot of the airplane looks downward at
any object on the ground then the angle
between his line of sight and horizontal line
drawn away from his eyes is called ANGLE OF
DEPRESSION.