Download Chapter 7 Homework

MATH 142 - Chapter 7 Homework (4906255)
Question
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Description
This homework assignment covers Chapter 7: 7.1, 7.2, 7.3... Please work as many
problems as possible and turn in your work by the due date. Late homework is NOT
accepted. As always, if you need anything, please email me
Joshua.Patterson@tamuc.edu
1.
Question Details
SPreCalc6 7.1.001. [1719016]
An equation is called an identity if it is valid for
2
2
sin x + cos x =
2.
-
value(s) of the variable. The equation 2x = x + x is an algebraic identity, and the equation
is a trigonometric identity.
Question Details
SPreCalc6 7.1.003. [2703771]
-
SPreCalc6 7.1.004. [2703858]
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SPreCalc6 7.1.008.MI. [2678482]
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SPreCalc6 7.1.009. [2703875]
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SPreCalc6 7.1.010. [2705111]
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SPreCalc6 7.1.011. [2703846]
-
Write the trigonometric expression in terms of sine and cosine, and then simplify.
4 cos t tan t
3.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
cos t csc t
4.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
sec x
csc x
5.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
cos u cot u + sin u
6.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
2
2
sin θ (1 + cot θ)
7.
Question Details
Write the trigonometric expression in terms of sine and cosine, and then simplify.
cos θ − sec θ
sin θ
8.
Question Details
SPreCalc6 7.1.013-026.502.XP.MI. [1870977]
-
Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.
2
2
2
3 sin x csc x − 3 sin x
9.
Question Details
SPreCalc6 7.1.013. [2703857]
-
SPreCalc6 7.1.015. [2703802]
-
SPreCalc6 7.1.017. [2703798]
-
SPreCalc6 7.1.057. [2705097]
-
SPreCalc6 7.1.058. [1719003]
-
Simplify the trigonometric expression.
2 sin x sec x
tan x
10.
Question Details
Simplify the trigonometric expression.
1 + cos y
sec y + 1
11.
Question Details
Simplify the trigonometric expression.
2
csc x − 1
2
csc x
12.
Question Details
Verify the identity.
2
cos x − 1
−sin x
=
2
cos x + 1
(cos x + 1)
Multiply the numerator and denominator by a common value, and then simplify.
cos x − 1
=
cos x + 1
cos x − 1
cos x + 1
cos x + 1
=
(cos x + 1)
2
Use a Pythagorean Identity.
=
13.
Question Details
Verify the identity.
cos w
cot w
=
cos w + sin w
1 + cot w
14.
Question Details
SPreCalc6 7.1.062. [1719017]
-
SPreCalc6 7.1.066. [1719027]
-
SPreCalc6 7.1.077. [2705081]
-
SPreCalc6 7.1.084. [1719252]
-
SPreCalc6 7.2.003. [2708358]
-
Verify the identity.
2
1 + sec x
2
= cos x + 1
2
1 + tan x
15.
Question Details
Verify the identity.
cos A
− tan A = sec A
1 − sin A
16.
Question Details
Verify the identity.
2
2
sin t + cot t − 1
2
2
= cot t
cos t
Use the Pythagorean and Reciprocal Identities to simplify.
2
2
2
sin t + cot t − 1
2
+ cot t
=
cos t
2
cos t
1
=
2
cos t
+
2
1
2
cos t
cos t
sin t
2
1
=
+
=
+ csc t
2
sin t
2
=
17.
Question Details
Verify the identity.
1 + cot x
tan x + 1
=
1 − cot x
tan x − 1
18.
Question Details
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
sin 75°
19.
Question Details
SPreCalc6 7.2.006. [2708244]
-
SPreCalc6 7.2.007. [2708334]
-
SPreCalc6 7.2.012.MI. [2678435]
-
SPreCalc6 7.2.015. [2708250]
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SPreCalc6 7.2.016.MI. [2725681]
-
SPreCalc6 7.2.017. [2708345]
-
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
cos 75°
20.
Question Details
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
tan 75°
21.
Question Details
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
sin −
22.
5π
12
Question Details
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
cos 19° cos 26° − sin 19° sin 26°
Find its exact value.
23.
Question Details
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
cos 15° cos 75° − sin 15° sin 75°
Find its exact value.
24.
Question Details
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
cos
4π
5
cos
Find its exact value.
7π
15
+ sin
4π
5
sin
7π
15
25.
Question Details
SPreCalc6 7.2.019. [2708367]
-
SPreCalc6 7.2.020.MI. [2708352]
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SPreCalc6 7.2.032. [1767135]
-
SPreCalc6 7.2.034.MI. [2678438]
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SPreCalc6 7.2.036. [1759351]
-
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
tan 41° − tan 11°
1 + tan 41° tan 11°
Find its exact value.
26.
Question Details
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
cos
13π
15
cos −
π
5
− sin
13π
15
sin −
π
5
Find its exact value.
27.
Question Details
Prove the identity.
tan x −
28.
π
4
=
tan x − 1
tan x + 1
Question Details
Prove the identity.
3 cos(x + y) + 3 cos(x − y) = 6 cos x cos y
29.
Question Details
Prove the identity.
cot(x + y) =
cot y cot x − 1
cot x + cot y
30.
Question Details
If we know the values of sin x and cos x, we can find the value of sin 2x by using the
State the formula: sin 2x =
31.
SPreCalc6 7.3.002. [2708389]
-
.
If we know the value of cos x and the quadrant in which x/2 lies, we can find the value of sin (x/2) by using the
32.
-
Formula for Sine.
Question Details
State the formula: sin(x/2) = ±
SPreCalc6 7.3.001. [2708790]
Formula for Sine.
.
Question Details
SPreCalc6 7.3.004. [2708211]
-
SPreCalc6 7.3.006.MI. [2678458]
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SPreCalc6 7.3.008. [2708231]
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SPreCalc6 7.3.009. [2708228]
-
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −
12
,
5
x in Quadrant II
sin 2x =
cos 2x =
tan 2x =
33.
Question Details
Find sin 2x, cos 2x, and tan 2x from the given information.
csc x = 6,
tan x < 0
sin 2x =
cos 2x =
tan 2x =
34.
Question Details
Find sin 2x, cos 2x, and tan 2x from the given information.
sec x = 8,
x in Quadrant IV
sin 2x =
cos 2x =
tan 2x =
35.
Question Details
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −
sin 2x =
cos 2x =
tan 2x =
1
,
2
cos x > 0
36.
Question Details
SPreCalc6 7.3.017. [2709806]
-
SPreCalc6 7.3.018. [2708984]
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SPreCalc6 7.3.019. [2709011]
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SPreCalc6 7.3.020.MI. [2708969]
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SPreCalc6 7.3.021. [2709729]
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SPreCalc6 7.3.025. [2709702]
-
SPreCalc6 7.3.029. [2709809]
-
Use an appropriate Half-Angle Formula to find the exact value of the expression.
sin 15°
37.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression.
tan 15°
38.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression.
tan 22.5°
39.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression.
sin 75°
40.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression.
cos 165°
41.
Question Details
Use an appropriate Half-Angle Formula to find the exact value of the expression.
sin
42.
π
8
Question Details
Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
(a)
2 sin 17° cos 17°
(b)
2 sin 4θ cos 4θ
43.
Question Details
SPreCalc6 7.3.030. [2708995]
-
SPreCalc6 7.3.031. [2709022]
-
SPreCalc6 7.3.032. [2709016]
-
SPreCalc6 7.3.033. [2710491]
-
Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
(a)
(b)
44.
2 tan 9°
2
1 − tan 9°
2 tan 9θ
2
1 − tan 9θ
Question Details
Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
45.
2
2
(a)
cos 35° − sin 35°
(b)
cos 4θ − sin 4θ
2
2
Question Details
Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
46.
2
(a)
cos
(b)
2 sin
θ
2
θ
2
− sin
cos
2
θ
2
θ
2
Question Details
Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
(a)
(b)
Assignment Details
sin 6°
1 + cos 6°
1 − cos 6θ
sin 6θ