Calculus questions on trigonometric functions

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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

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.–/3.84 pointsLarPreCalcRMRPAlt6 6.4.020.My Notes

Question Part
Points

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

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.–/3.84 pointsLarPreCalcRMRPAlt6 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,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._x000D_ $ _x000D_ sinleft(dfrac{{color{red}2}pi}{9}right)cosleft(dfrac{{color{red}5}pi}{8}right) + cosleft(dfrac{{color{red}2}pi}{9}right)sinleft(dfrac{{color{red}5}pi}{8}right)_x000D_ $ _x000D_

12.–/3.84 pointsLarPreCalcRMRPAlt6 6.5.046.My Notes

Question Part
Points

Use the figure to find the exact value of each trigonometric function.WebAssign Plot

(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)

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