calculus-questions-on-trigonometric-functions
Find the exact value of the trigonometric expression given that
12 |
13 |
cos v = −
15 |
17 |
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 half-angle formulas.
sec(u) = − |
|
, |
|
< u < π |
sin(
u/2) =
cos(
u/2) =
tan(
u/2) =
3.–/3.84 pointsLarPreCalcRMRPAlt6 6.4.032.My Notes
Write the expression as the sine, cosine, or tangent of an angle.sin(16°)cos(77°) + cos(16°)sin(77°)
4.–/3.84 pointsLarPreCalcRMRPAlt6 6.5.022.My Notes
Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.
cos u = −
12 |
13 |
,
Ï€ |
2 |
<
u <
Ï€
sin 2u | = | |
cos 2u | = |
|
tan 2u | = |
|
5.LarPreCalcRMRPAlt6 6.4.050.My Notes
Question Part |
Points |
Find the exact value of the trigonometric expression given that sin u =
15 |
17 |
and
cos v = −
20 |
29 |
. (Both
u and
v are in Quadrant II.)
cos(v − u)
6.LarPreCalcRMRPAlt6 6.4.020.My Notes
Question Part |
Points |
Find the exact values of the sine, cosine, and tangent of the angle.
7Ï€ |
12 |
=
Ï€ |
3 |
+
Ï€ |
4 |
sin
|
|
||
cos
|
|
||
tan
|
|
7.LarPreCalcRMRPAlt6 6.4.056.My Notes
Question Part |
Points |
Find the exact value of the trigonometric expression given that sin u = −
20 |
29 |
and
cos v = −
7 |
25 |
. (Both
u and
v are in Quadrant III.)
cos(u − v)
8.LarPreCalcRMRPAlt6 6.5.058.My Notes
Question Part |
Points |
Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.cot u = 2,Ï€ < u < 3Ï€/2
sin(u/2) | = | |
cos(u/2) | = |
|
tan(u/2) | = |
|
9.–/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 half-angle formulas.
cos u =
5 |
13 |
,0 <
u <
Ï€/2
sin(u/2) | = | |
cos(u/2) | = |
|
tan(u/2) | = |
|
10.–/3.84 pointsLarPreCalcRMRPAlt6 6.4.034.My Notes
Write the expression as the sine, cosine, or tangent of an angle.
tan(62°) − tan(54°) |
1 + tan(62°)tan(54°) |
11.–/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
θ |
2 |
(b)
cos
θ |
2 |
(c)
tan
θ |
2 |
(d)
cot
θ |
2 |
(e)
sec
θ |
2 |
(f)
csc
θ |
2 |
(g)
2 sin
θ |
2 |
cos
θ |
2 |
(h)
2 cos
θ |
2 |
tan
θ |
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 = −
40 |
41 |
. (Both
u and
v are in Quadrant II.)
sin(u − v)