Download MAP4C Cos 150o:_Cos_o Tan 150 o: Tan o

MAP4C
Sec.1.3
Sine, Cosine and Tangent of Obtuse Angles
"
-
When point P (x,y) is in Quadrantl, lA is an acute angle (ie: between 0 o and 90
trigonometric ratios Sin A is positive, Cos A is positive and Tan A is positive.
"). the three primary
When point P (x,y) is in QuadrantlI, lA is an obtuse angle (ie: between 90 o and 180
trigonometric ratios Sin A is positive, Cos A is negative and Tan A is negative.
).
The three primary
Investigation:
1.
Complete the following table. Evaluate each ratio (Sin A, Cos A and Tan A) to 4 decimal places.
Ansle A
20
50
Sin A
Cos A
Tan A
200
670
79o
930
970
0
101
0
113
0
160
175'
179
o
2. Which pairs of angles have the same value for the Sin A. How are these angles related?
3. What do you notice about the values of Cos A for the pairs of angles that you identified in the previous
question?
4.
What do you notice about the values of Tan A for the pairs of angles that you identified in the previous
question?
We can apply these results to any obtuse angle. For example;
o
:
_o
Cos 150o:_Cos_o
Tan 150 o:
Tan
Sin 150
Sin
o
..
ihis means that whenthe Sin of an angle is positive, the angle could be in the first quadrant
second quadrant (ie: obtuse):
Page 1 of2
(ie:
acute) or in the
MAP4C
Ex.l:
Suppose
Sin 157
Ex.2:
Sec.1.3
ZC = 157'. Determine each of the trigonometric ratios for angle C,to 4 decimal places.
o:
Sin o
Cos 157
o:
Cos o
T
an
157
o
:
Tan
o
A is between 0 o and 180 o. In each case, state whether angle A is acute or obtuse, or
whether two possible angles might exist. Then determine the measure(s) of A to the nearest degree.
Suppose angle
a)
CorA=-1
84
Ex.3:
Find the following angles;
a)
The Sin P
b)
The Cos
c)
The Tan R
Page 2 of 2
:
SinA=1
0.65 , is angle P acute, obtuse, neither or both? Find the value(s) of angle P?
Q:0.22, is angle Q acute, obtuse, neither
:
b)
or both? Find the value(s) of angle Q?
-0.44, is angle R acute, obtuse, neither or both? Find the value(s) of angle R?