Cofunctions Review:
The value of the sine of an acute angle is the same as the value of the
cosine of the complement of that angle. The opposite is true also; the
value of the cosine of an acute angle is the same as the value of the
sine of the complement of that angle.
Answer:
cos(7π/18)
The other Objective Review:
Given the decimal approximate, find the original angle (nearest tenth):
Question:
Calculator Instructions:
Answer:
sin   .7193
for 0    360
*place calculator in degree mode
*2nd SIN
* sin
1
(.7193)
46.0 QI
Where else is sine positive within the given range?
Since sine is also positive in QII an additional angle within the given range also gives a correct
answer. Using your knowledge of reference angles gives:   180  46  134
So there are two answers within the given range: 46.0º and 134.0º
Given the decimal approximate, find the original angle ( nearest tenth):
Question:
Calculator Instructions:
Answer:
tan   .2309 for
0   <360
*place calculator in degree mode
*2nd TAN
* tan
1
(.2309)
-13.0º
?
**347º QIV
**The calculator answer is not within the given range and can’t be considered. However, we can
find the angle Coterminal to –13.0º by adding 360º. So one of the angles within the given range
is 347º (this is illustrated in red on the drawing below). You will learn why the calculator gave a
negative reference angle when you study Inverse Trig Functions later in this course. It is
important to realize that the reference angle (by definition) for -13º is actually 13º. This fact is
necessary in finding the other angle of interest in this problem.
Where else is tangent negative within the given range?
Since tangent is also negative in QII, use the reference angle 13º to find the other angle that
evaluates the given decimal approximation. This is illustrated in aqua on the image above. So
the two angles that make the given decimal approximation true within the given range are: 167º
and 347º. Check these on the graphics calculator.
Try Another One:
Given the decimal approximate, find the original angle ( nearest hundredth):
Question:
Calculator Instructions:
0   <2
*place calculator in radian mode
cos   0.4611 for
1
* cos (.4611)
Answer:
2.05 QII
Before finding the other angle that makes the decimal approximate true within the given range,
find the reference angle using the procedures taught previously. Since the answer is in QII,
perform the following:   2.05  1.09
So where else is cosine negative?
Cosine is also negative in QIII. Using reference angle rules, the second answer was determined
(this is illustrated in red above). So the radian angles that evaluate the given decimal
approximation within the given range are 2.05 radians and 4.23 radians.