calculusquestionsontrigonometricfunctions1
Find the exact value of the trigonometric expression given that sin u = âˆ’
12 
13 
and
cos v = âˆ’
15 
17 
. (Both
u and
v are in Quadrant III.)
tan(u + v)
2.LarPreCalcRMRPAlt6 6.5.060.My Notes
Question Part 
Points 
Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the halfangle formulas.
sec(u) = âˆ’ 

, 

< u < Ï€ 
sin(
u/2) =
cos(
u/2) =
tan(
u/2) =
3.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.4.032.My Notes
Write the expression as the sine, cosine, or tangent of an angle.sin(16Â°)cos(77Â°) + cos(16Â°)sin(77Â°)
4.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.5.022.My Notes
Find the exact values of sin 2u, cos 2u, and tan 2u using the doubleangle formulas.
cos u = âˆ’
12 
13 
,
Ï€ 
2 
<
u <
Ï€
sin 2u  =  
cos 2u  = 

tan 2u  = 

5.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.4.050.My Notes
Find the exact value of the trigonometric expression given that sin u =
15 
17 
and
cos v = âˆ’
20 
29 
. (Both
u and
v are in Quadrant II.)
cos(v âˆ’ u)
6.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.4.020.My Notes
Find the exact values of the sine, cosine, and tangent of the angle.
7Ï€ 
12 
=
Ï€ 
3 
+
Ï€ 
4 
sin
= 


cos
= 


tan
= 

7.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.4.056.My Notes
Find the exact value of the trigonometric expression given that sin u = âˆ’
20 
29 
and
cos v = âˆ’
7 
25 
. (Both
u and
v are in Quadrant III.)
cos(u âˆ’ v)
8.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.5.058.My Notes
Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the halfangle formulas.cot u = 2,Ï€ < u < 3Ï€/2
sin(u/2)  =  
cos(u/2)  = 

tan(u/2)  = 

9.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.5.056.My Notes
Find the exact values of sin(u/2), cos(u/2), and tan(u/2)
using the halfangle formulas.
cos u =
5 
13 
,0 <
u <
Ï€/2
sin(u/2)  =  
cos(u/2)  = 

tan(u/2)  = 

10.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.4.034.My Notes
Write the expression as the sine, cosine, or tangent of an angle.
tan(62Â°) âˆ’ tan(54Â°) 
1 + tan(62Â°)tan(54Â°) 
11.â€“/3.84 pointsLarPreCalcRMRPAlt6 6.4.038.My Notes
Write the expression as the sine, cosine, or tangent of an angle.
12.LarPreCalcRMRPAlt6 6.5.046.My Notes
Question Part 
Points 
Use the figure to find the exact value of each trigonometric function.
(a)sin
Î¸ 
2 
(b)
cos
Î¸ 
2 
(c)
tan
Î¸ 
2 
(d)
cot
Î¸ 
2 
(e)
sec
Î¸ 
2 
(f)
csc
Î¸ 
2 
(g)
2 sin
Î¸ 
2 
cos
Î¸ 
2 
(h)
2 cos
Î¸ 
2 
tan
Î¸ 
2 
13.LarPreCalcRMRPAlt6 6.4.052.My Notes
Question Part 
Points 
Find the exact value of the trigonometric expression given that sin u =
5 
13 
and
cos v = âˆ’
40 
41 
. (Both
u and
v are in Quadrant II.)
sin(u âˆ’ v)