7-3: COMPUTING THE VALUES OF TRIG FUNCTIONS
In a right triangle, if one of the acute angles = 45, then so does the other; and the triangle is
isosceles and could have legs = 1, hypotenuse = 2 . In a right triangle, if one of the acute
angles is 30, then the other is 60; such a triangle could have a hypotenuse of 2 and legs of 1
and 3 . Find the exact value of the six trigonometric functions of 45, 30, and 60:
Sine
Cosine
Tangent
Cotangent
Cosecant
Secant

45= /4
30=/6
60=/3
Find the exact value of each expression if  = 30; do not use a calculator:
1.
tan  2 
2. 3 sec 
3.
sin
3
Find the exact value of each expression; do not use a calculator:
3. 4 sin 45 + 2 cos 30
4. 5 tan 30 . sin 60
5. 1 + sec2 45 - cos2 60
Use a calculator to find the approximate value of each expression; round to 2 decimal places:
6. cos 42
7. sec 38
8. csc 72
9. sin  (use radian mode)
8
10. cot 5
14
11. tan 42.859
EXTRA PRACTICE– 7.3, PG. 536-539
Find exact value; no calculator:
1. sin 30.tan 60
2. 1 + tan2 30 - csc2 45
Use calculator; approximate to 2 decimal places
3.
csc 55
38. cot

18
EXTRA PRACTICE – 7.4, PG. 548-536:
 1 3
1. Find 6 trig functions:
  ,

 2 2 
sin  = ____________
cos  = ____________
tan  = ____________
csc  = ____________
sec  = ____________
cot  = ____________
2. Find exact value, show reference angle; no calculator: csc
3. Find exact value, show reference angle; no calculator: tan
9
2
8
3
4. Find exact value of remaining trig functions: cos  = 4/5, 270 <  360 Quadrant 4
sin  = ____________
tan  = ____________
csc  = ____________
sec  =
____________
5. Find the exact value of tan 60 + tan 150
cot  = ____________
6.4 TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES
Let  be any angle in standard position and let (a, b) denote any point except the origin on the
terminal side of . If r  a 2  b 2 denotes the distance from (0, 0) to (a, b), then the six trigonometric
functions of  are defined as the following ratios:
b
r
r
1
csc  
b sin
a
b sin
tan  
r
a cos
r
1
a
1
cos
sec  
cot   

a cos
b tan sin
Quandrantal angles are angles whose terminal side lies on the x- or y-axis, such as 0, 90, 180, 270,
and 360. Their trig function values will always be 0, 1, or undefined.
sin 
cos 
A point on the terminal side of an angle  is given. Find the exact value of the six trigonometric
functions of the angle :
1
2
(a, b)
(-1, -2)
r
sin
cos
tan
csc
sec
cot
 1 3
 ,

 2 2 
Name the quadrant in which each angle lies: All Seniors Take Calculus
Sin  > 0
Sin  > 0
Cos  < 0
Cos  > 0
Tan  < 0
Tan  > 0
Sin  < 0
Sin  < 0
Cos  < 0
Cos  > 0
Tan  > 0
Tan  < 0
3. sin  > 0, cos < 0
4. tan  < 0, sec > 0
5. csc < 0, cot > 0
Two angles in standard position are coterminal if they have the same terminal side. If  is a nonacute angle, the acute angle formed by the terminal side of  and the  x-axis is called the reference
angle for . A general angle  and its coterminal reference angle  have the same values of their trig
functions except for the sign, which depends the quadrant in which it lies. Find the exact value of
each expression without a calculator:
6-9.
sin  3 
cos (-420)
sec 630
csc 9
2
Quadrant
Reference Angle
Exact Value
Find the exact value of each of the remaining trigonometric functions of :
10-11.
Cot  < 0
IV
Quadrant
(a, b), r
Sin 
Cos 
Tan 
Csc 
Sec 
Cot 
12. If cos  = -2, find cos ( + )
3
5
3