Thus, by figuring out the cos (adja-
cent/hypotenuse) and sin (opposite/
hypotenuse) for the angle 60°, Q is at
point (1/2, 3 /2) on the circle. The
other trig functions can be determined
using the methods in the questions
above:
cos
1/2 (x)
sin 3 /2 (y)
tan 3 ( 3 /1, or y/x)
sec
2 (1 / 1/2, or 1/x)
csc
2/ 3 (1/y)
cot
1/ 3 (x/y)What are some identities in
trigonometry?
There are many fundamental identities—
an equation that is true regardless of
what values are substituted for any of the
variables—based on trigonometric func-
tions. Because there are relationships between the trig functions, identities can be
used to rewrite equations, allowing the user to simplify or get more information out of
an equation. The identities include reciprocal identities, ratio identities, periodicity
identities, Pythagorean identities, odd-even identities, sum-difference identities, dou-
ble angle identities, half angle identities, and several more. The following lists a few
such identities:
Pythagorean Identities- cos^2
sin^2
1 - tan^2
1 sec^2 - cot^2
1 csc^2
Reciprocal Identities - sin
1/csc - cos
1/sec - tan
1/cot - sec
1/cos - csc
1/sin - cot
1/tan
Ratio (or Quotient) Identities - tan
sin /cos - cos
cos /sin 203
GEOMETRY AND TRIGONOMETRY
In this example, to find the trig functions of an angle
of 60 degrees, draw a triangle with point O at the
center of a circle with radius 2; use the
Pythagorean Theorem to determine the length of
the line dropping down at a right angle from point
Q; and then calculate the trig functions using these
measurements.