Calculus Questions on trigonometric Functions

Find the exact value of the trigonometric expression given that sin u = −

12

13

and

cos v = −

15

17

. (Both
u and
v are in Quadrant III.)

tan(u + v)

2.–/3.84 pointsLarPreCalcRMRPAlt6 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) = −

11 5

,

π 2

< 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

,

π

2

<
u <
π

sin 2u	=
cos 2u	=
tan 2u	=

5.–/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 = −

20

29

. (Both
u and
v are in Quadrant II.)

cos(v − u)

6.–/3.84 pointsLarPreCalcRMRPAlt6 6.4.020.My Notes

Find the exact values of the sine, cosine, and tangent of the angle.

7π

12

=

π

3

+

π

4

sin 7π 12 =
cos 7π 12 =
tan 7π 12 =

7.–/3.84 pointsLarPreCalcRMRPAlt6 6.4.056.My Notes

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.–/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 half-angle formulas.cot u = 2,π < u < 3π/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 <
π/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.–/3.84 pointsLarPreCalcRMRPAlt6 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.–/3.84 pointsLarPreCalcRMRPAlt6 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)