Download Document

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  = 60; do not use a calculator:
1.
tan

2. 3 csc 
3.
2
Find the exact value of each expression; do not use a calculator:
4. 4 sin 45 + 2 cos 30
5. 5 tan 30 . sin 60
cos
3
6. 1 + sec2 45 - cos2 60
Use a calculator to find the approximate value of each expression; round to 2 decimal places:
7. cos 42
8. sec 38
9. csc 72
10. sin  (use radian mode)
8
11. cot 5
12. tan 42.859
14
Projectile Motion, fired at inclination  and initial speed v0 (g  32.2 ft/sec2  9.8 m/sec2:
2
2
2
Horizontal distance: R  2v0 sin cos
Height: H  v0 sin 
g
2g
13. Find the range R and maximum height H of a projectile fired at an angle of 40 to the
horizontal with an initial speed of 300 m/sec.
14 In a certain piston engine, the distance x (in meters) from the center of the drive shaft to the
head of the piston, where  is the angle between the crank and the path of the piston head by
the formula below. Find x when  = 35.
x  cos  16  0.5 2cos 2   1

6/29/2017

7.4 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 :
(a, b)
r
sin
cos
tan
csc
sec
cot
1 (-1, -2)
2
 1 3
 ,

 2 2 
Name the quadrant in which each angle lies: All Seniors Take Calculus
3.
sin  > 0, cos < 0
Sin  > 0
Sin  > 0
Cos  < 0
Cos  > 0
Tan  < 0
Tan  > 0
Sin  < 0
Sin  < 0
Cos  < 0
Cos  > 0
Tan  > 0
Tan  < 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 . Find the reference angle of each angle and name its quadrant:
7
6. 300
7. -490
8.
9. 3

4
2
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:
10 – 13.
sin  3 
cos (-420)
sec 630
csc 9
2
Quadrant
Reference Angle
Exact Value
6/29/2017
Find the exact value of each of the remaining trigonometric functions of :
14 – 16.
Cot  < 0
Tan  > 0
IV
Quadrant
(a, b), r
Sin 
Cos 
Tan 
3
5
Csc 
Sec 
Cot 
17. If cos  = -2, find cos ( + )
18. If tan  = 5, find tan ( + )
6/29/2017
3