Download 6. More about Trigonometry

6. More about Trigonometry
(a) How to memorize the trigonometric identities?
Trigonometric Identities Easy Memory Tips:
Convert the trigonometric ratios with the
angles 180o± and 360o± .
The symbol of sine/cosine/tangent remains
unchanged. Write the angle as . According to
the quadrant that the angle lies in, determine the
sign of the trigonometric ratio.
Only sin
is +ve
Only tan
is +ve
All ratio
are +ve
S
A
T
C
Only cos
is +ve
Quadrant
II
III
IV
I
 is acute
180 -
o
180 +
360o-
360o+
sinsin
sin
sin 
- sin 
- sin 
sin 
coscos
cos
- cos 
- cos 
cos 
cos 
tantan
tan
- tan 
tan 
- tan 
tan 
o
6. More about Trigonometry
(a) How to memorize the trigonometric identities?
Trigonometric Identities Easy Memory Tips:
Convert the trigonometric ratios with the
angles 90o± and 270o± .
The symbol of sine/cosine/tangent is changed.
Write the angle as . According to the quadrant
that the angle lies in, determine the sign of the
trigonometric ratio.
Only sin
is +ve
Only tan
is +ve
All ratio
are +ve
S
A
T
C
Only cos
is +ve
Quadrant
I
II
III
IV
 is obtuse
90o-
90o+
270o-
270o+
sincos
sin
cos 
cos 
- cos 
- cos 
cos
sin 
1
tan 
- sin 
1
- tan

- sin 
1
tan
sin 
1
- tan

cossin
tan 1
tan
tan
6. More about Trigonometry
(b) For 0 ≤ ≤360 , how to solve the trigonometric
equations?
o
E.g.
o
Solve the equation sin  = -0.5.
Consider sin  = 0.5 first.
+
 = 30o
(Use calculator to calculate the answer)
∵ sin  < 0
∴  lies in quadrants III or IV
+
Sin
All
S A
T C
180o+
∵ The symbol of sine does not change
-
∴ We only need to consider 180o+  and 360o-
i.e.  = 180o+30o or  = 360o-
30o
= 210o
or
= 330o
360o-
-