THE UNIVERSITY OF AKRON
Theoretical and Applied Mathematics
Memory Flash Cards
The Trigonometric Functions
Katie Jones
and
Tom Price
Begin
c 2002 teprice@uakron.edu
Last Revision Date: August 10, 2002
Version 1.0
Let P be the point on the unit circle with coordinates (x, y) that determines the angle in standard position
of measure t rad. Give the values of
sin t
Hint
and
Soln
tan t
Next
Let P be the point on the unit circle with coordinates (x, y) that determines the angle in standard position
of measure t rad. Give the values of
cot t
Hint
and
Soln
csc t
Next
Let P be the point on the unit circle with coordinates (x, y) that determines the angle in standard position
of measure t rad. Give the values of
cos t
Hint
and
Soln
sec t
Next
Express sec t in terms of another
trigonometric function.
Hint
Soln
Next
Express tan t in terms of other
trigonometric functions.
Hint
Soln
Next
Express cot t in terms of other
trigonometric functions.
Hint
Soln
Next
Give the values of
π
and
sin
4
Hint
Soln
π
sec .
4
Next
Give the value of
π
tan .
4
Hint
Soln
Next
Give the values of
π
and
tan
3
Hint
Soln
π
sec .
3
Next
Give the values of
π
and
sin
3
Hint
Soln
π
cot .
3
Next
Give the values of
π
and
cos
3
Hint
Soln
π
csc .
3
Next
Give the values of
π
and
cos
6
Hint
Soln
π
sin .
6
Next
Give the values of
π
and
tan
6
Hint
Soln
π
sec .
6
Next
Give the values of
π
and
cot
6
Hint
Soln
π
csc .
6
Next
5π
Give the values of sin 3π
4 and sec 4 .
Hint
Soln
Next
Give the value of tan −3π
4 .
Hint
Soln
Next
Give the values of
2π
and
tan
3
Hint
Soln
sec
Next
2π
.
3
Give the values of
−5π
and
sin
3
Hint
Soln
cot
−5π
.
3
Next
Give the values of
4π
and
cos
3
Hint
Soln
csc
Next
4π
.
3
Give the values of
5π
and
cos
6
Hint
Soln
sin
5π
.
6
Next
Give the values of
−π
and
tan
6
Hint
Soln
sec
Next
−π
.
6
Give the values of
−11π
and
cot
6
Hint
Soln
csc
−11π
.
6
Next
Give the values of
sin 30 ◦
and
Hint
Soln
tan 30 ◦ .
Next
Give the values of
cos (−60◦)
and
Hint
Soln
tan (−60◦) .
Next
Give the values of
sec 210◦ and
Hint
Soln
cot 210◦.
Next
Give the values of
sin (−135◦)
Hint
and cos (−135◦) .
Soln
Next
True or False:
tan t = tan (t − π)
Hint
Soln
Next
True or False:
sin(t + π) = − sin t
Hint
Soln
Next
True or False:
sin(t + π) = cos t
Hint
Soln
Next
True or False:
sin
Hint
π
= sin 135◦
4
Soln
Next
True or False:
cos (α + 360◦) = cos α
(Note: α represents a degree measure.)
Hint
Soln
Next
True or False:
tan (α + 90◦) = tan α
(Note: α represents a degree measure.)
Hint
Soln
Next
HINT
Recall that sin t is defied to be the ycoordinate of P. See the figure below.
y
P x ,y t
Soln
Next
x
Answer: sin t = y
and
tan t =
y
x
Next
HINT
Recall that
csc t =
Soln
1
.
sin t
Next
Answer: cot t =
x
y
and
csc t =
1
y
Next
HINT
Recall that cot t is defied to be the xcoordinate of P. See the figure below.
y
P x ,y t
Soln
Next
x
Answer: cos t = x
and
sec t =
1
x
Next
HINT
Recall that
sec t =
Soln
1
x
Next
Answer: sec t =
1
1
=
x cos t
Next
HINT
This question has two answers. Rey
call that tan t =
x
Soln
Next
Answer: tan t =
1
sin t
y
=
=
x cot t cos t
Next
HINT
This question has two answers. Rex
call that cot t =
y
Soln
Next
Answer: cot t =
1
cos t
x
=
=
y tan t sin t
Next
HINT
Recall that
sin
π
π
= cos
4
4
Soln
Next
Answer: sin π4 =
√1
2
and sec π4 =
√
2
Next
HINT
Recall that
sin
π
π
= cos
4
4
Soln
Next
Answer: tan π4 = 1
Next
HINT
Recall that
√
π
3
sin =
3
2
Soln
Next
Answer: tan π3 =
√
3 and sec π3 = 2
Next
HINT
Recall that
sin
π
π
= cos
3
6
Soln
Next
π
3
Answer: sin =
√
3
2
π
3
and cot =
√
3
3
Next
HINT
Recall that
sin
π
π
= cos
3
6
Soln
Next
Answer: cos π3 =
1
2
and csc π3 =
√2
3
Next
HINT
Recall that
sin
π
π
= cos
6
3
Soln
Next
π
6
Answer: cos =
√
3
2
and sin π6 =
1
2
Next
HINT
Recall that
√
π
3
sin =
6
2
Soln
Next
Answer: tan π6 =
√1
3
and sec π6 =
√2
3
Next
HINT
Recall that
tan
π
1
=√
6
3
Soln
Next
Answer: cot π6 =
√
3 and csc π6 = 2
Next
HINT
Recall that
sin
π
3π
= sin
4
4
Soln
Next
Answer: sin 3π
4 =
√1
2
√
and sec 5π
=
−
2
4
Next
HINT
Recall that
tan (−t) = − tan t
Soln
Next
Answer: tan −3π
4 = 1
Next
HINT
Recall that
√
2π
3
=
sin
3
2
Soln
Next
tan 2π
3
√Answer:
= − 3 and sec 2π
3 = −2
Next
HINT
Recall that
√
5π
3
=−
sin
3
2
Soln
Next
sin
−5π
3
Answer:
= 23 and cot −5π
3 =
√
√
3
3
Next
HINT
Recall that
cos
Soln
π 1
=
3 2
Next
1
4π
√2
Answer: cos 4π
3 = − 2 and csc 3 = − 3
Next
HINT
Recall that
sin
π
π
= cos
6
3
Soln
Next
Answer: cos
5π
6
=−
√
3
2
and sin 5π
6 =
1
2
Next
HINT
Recall that
sec
π
2
=√
6
3
Soln
Next
tan
−π
6
=
Answer:
and sec −π
6 =
− √13
√2
3
Next
HINT
Recall that
cot
−π
11π
= cot
6
6
Soln
Next
cot −11π
6
√ Answer:
= 3 and csc −11π
6 = 2
Next
HINT
Recall that
tan 30◦ = tan
Soln
Next
π
6
Answer: sin 30◦ =
1
2
and tan 30◦ =
√1
3
Next
HINT
Recall that
sin (−60◦) = − sin 60◦
Soln
Next
◦
sin (−60 ) =
√ Answer:
− 23 and
√
tan (−60 ) = − 3
◦
Next
HINT
Recall that
sec 210◦ = −
Soln
1
cos 30◦
Next
Answer:
√
sec 210◦ = − √23 and cot 210◦ = 3
Next
HINT
Recall that
sin (−135◦) = − sin 135◦
Soln
Next
◦
sin (−135 ) =
√Answer:
− 22 and
◦
cos (−135 ) : −
Next
√
2
2
HINT
The period of the tangent function is
π.
Soln
Next
Answer: T RU E
Next
HINT
Envision a figure depicting the angles
of measure (t + π) rad and t rad .
Soln
Next
Answer: T RU E
Next
HINT
Envision a figure depicting the angles
of measure (t + π) rad and t rad .
Soln
Next
Answer: F ALSE
Next
HINT
Recall that
3π
rad = 135◦
4
Soln
Next
Answer: T RU E
Next
HINT
The period of the cosine function is
2π.
Soln
Next
Answer: T RU E
Next
HINT
Envision a figure depicting the angles
of measure (α + 90◦) and α.
Soln
Next
Answer: F ALSE
Next