TI 84 - Viewscreen Calc, Quick Manual

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© Texas Instruments, 2007
Trigonometry with the TI-84 Plus Silver Edition
Trigonometric Functions
Acute Angles
ò
sin
␪
= opp/hyp csc
␪
= hyp/opp
ô
cos
␪
= adj/hyp sec
␪
= hyp/adj
ö
tan
␪
= opp/adj cot
␪
= adj/opp
Arbitrary Angles
sin
␪
= b/r csc
␪
= r/b
cos
␪
= a/r sec
␪
= r/a
tan
␪
= b/a cot
␪
= a/b
Real Numbers
sin t = y csc t = 1/y
cos t = x sec t = 1/x
tan t = y/x cot t = x/y
Special Triangles
Trigonometric Identities
csc t = 1/sin t tan t = sin t/cos t
sec t = 1/cos t cot t = cos t/sin t
cot t = 1/tan t
sin
2
t + cos
2
t = 1 sin (–t) = –sin t
1 + tan
2
t = sec
2
t cos (–t) = cos t
1 + cot
2
t = csc
2
t tan (–t) = –tan t
sin (u + v) = sin u cos v + cos u sin v
cos (u + v) = cos u cos v – sin u sin v
tan (u + v) =
sin (u – v) = sin u cos v – cos u sin v
cos (u – v) = cos u cos v + sin u sin v
tan (u – v) =
sin 2u =2 sin u cos u
cos 2u = cos
2
u – sin
2
u = 1 – 2 sin
2
u = 2 cos
2
u – 1
tan 2u =
sin = cos =
tan = = tan 2 u =
sin
2
u = cos
2
u =
sin u cos v =
1/
2
[sin (u + v) + sin (u – v)]
cos u sin v =
1/
2
[sin (u + v) – sin (u – v)]
cos u cos v =
1/
2
[cos (u + v) + cos (u – v)]
sin u sin v =
1/
2
[cos (u – v) – cos (u + v)]
opp
y
r
(a,b)
x
adj
u
u
hyp
1
1
π
4
y
t
(1,0)
t radians
(x,y)
x
=45
°
1
√
3
π
6
2
40
°
60
°
60
°
4
2
c
3
b
=30
°
π
3
=60
°
√
2
90
°
270
°
300
°
240
°
315
°
225
°
330
°
210
°
0
°
180
°
30
°
150
°
45
°
135
°
60
°
120
°
(0,1)
(1,0)
(0,-1)
(-1,0)
(
,
)
1
√
3
2 2
(
,
)
1
√
3
2 2
(
, -
)
1
√
3
2 2
(
, -
)
1
√
3
2 2
(
,
)
√
2
√
2
2 2
(
,
-
-
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
,
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
-
-
-
)
√
3 1
2 2
opp
y
r
(a,b)
x
adj
u
u
hyp
1
1
π
4
y
t
(1,0)
t radians
(x,y)
x
=45
°
1
√
3
π
6
2
40
°
60
°
60
°
4
2
c
3 b
=30
°
π
3
=60
°
√
2
90
°
270
°
300
°
240
°
315
°
225
°
330
°
210
°
0
°
180
°
30
°
150
°
45
°
135
°
60
°
120
°
(0,1)
(1,0)
(0,-1)
(-1,0)
(
,
)
1
√
3
2 2
(
,
)
1
√
3
2 2
(
, -
) 1
√
3
2 2
(
, -
) 1
√
3
2 2
(
,
)
√
2
√
2
2 2
(
,
-
-
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
,
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
-
-
-
)
√
3 1
2 2
opp
y
r
(a,b)
x
adj
u
u
hyp
1
1
π
4
y
t
(1,0)
t radians
(x,y)
x
=45
°
1
√
3
π
6
2
40
°
60
°
60
°
4
2
c
3 b
=30
°
π
3
=60
°
√
2
90
°
270
°
300
°
240
°
315
°
225
°
330
°
210
°
0
°
180
°
30
°
150
°
45
°
135
°
60
°
120
°
(0,1)
(1,0)
(0,-1)
(-1,0)
(
,
)
1
√
3
2 2
(
,
)
1
√
3
2 2
(
, -
) 1
√
3
2 2
(
, -
) 1
√
3
2 2
(
,
)
√
2
√
2
2 2
(
,
-
-
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
,
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
-
-
-
)
√
3 1
2 2
opp
y
r
(a,b)
x
adj
u
u
hyp
1
1
π
4
y
t
(1,0)
t radians
(x,y)
x
=45
°
1
√
3
π
6
2
40
°
60
°
60
°
4
2
c
3 b
=30
°
π
3
=60
°
√
2
90
°
270
°
300
°
240
°
315
°
225
°
330
°
210
°
0
°
180
°
30
°
150
°
45
°
135
°
60
°
120
°
(0,1)
(1,0)
(0,-1)
(-1,0)
(
,
)
1
√
3
2 2
(
,
)
1
√
3
2 2
(
, -
) 1
√
3
2 2
(
, -
) 1
√
3
2 2
(
,
)
√
2
√
2
2 2
(
,
-
-
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
,
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
-
-
-
)
√
3 1
2 2
tan u + tan v
1 – tan u tan v
tan u – tan v
1 + tan u tan v
2 tan u
1 – tan 2 u
1 – cos u
sin u
sin u
1 + cos u
u
2
1 – cos 2u
2
1 + cos 2u
2
u
2
1 – cos u
2
u
2
1 + cos u
2
√
√
Special Values of Trigonometric Functions
␪␪ ␪␪
(degrees) (radians)
sin
␪␪
cos
␪␪
tan
␪␪
cot
␪␪
sec
␪␪
csc
␪␪
0° 0 0 1 0 – 1 –
30° 2
45° 1 1
60° 2
90° 1 0 – 0 – 1
π
6
1
2
√
3
2
√
3
3
√
3
2
√
3
3
π
4
√
2
2
√
2
2
√
2
√
2
√
3
2
1
2
√
3
√
3
3
2
√
3
3
π
2
Laws of Sines and Cosines
Sine Cosine
sin A = sin B = sin C a 2 = b 2 + c 2 – 2bc cos A
a b c
c
2
= a
2
+ b
2
– 2ab cos C
b
2
= c
2
+ a
2
– 2ac cos B
Unit Circle
opp
y
r
(a,b)
x
adj
u
u
hyp
1
1
π
4
y
t
(1,0)
t radians
(x,y)
x
=45
°
1
√
3
π
6
2
40
°
60
°
60
°
4
2
c
3
b
=30
°
π
3
=60
°
√
2
90
°
270
°
300
°
240
°
315
°
225
°
330
°
210
°
0
°
180
°
30
°
150
°
45
°
135
°
60
°
120
°
(0,1)
(1,0)
(0,-1)
(-1,0)
(
,
) 1
√
3
2 2
(
,
) 1
√
3
2 2
(
, -
)
1
√
3
2 2
(
, -
)
1
√
3
2 2
(
,
)
√
2
√
2
2 2
(
,
-
-
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
, -
)
√
2
√
2
2 2
(
,
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
)
√
3 1
2 2
(
, -
-
-
-
)
√
3 1
2 2
π
3
Inverse Trigonometric Functions
Function Domain Range
y ?
y = sin
-1
x –1
≤
x
≤
1 –
≤
y
≤
y @
y = cos
-1
x –1
≤
x
≤
1 0
≤
y
≤ π
y A
y = tan
-1
x
All real numbers
– < y <
y = cot
-1
x
All real numbers
0 < y <
π
y = sec -1 x x
≥
1 0,
∪
y = csc
-1
x x
≥
1 – , 0
∪
0,
π
2
π
2
π
2
π
2
π
2
π
2
π
2
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1 - cos 2u
1 + cos 2u
π
2
,
π