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
[email protected]
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]
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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]
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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]
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SPreCalc6 7.2.012.MI. [2678435]
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SPreCalc6 7.2.015. [2708250]
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SPreCalc6 7.2.016.MI. [2725681]
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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]
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SPreCalc6 7.2.034.MI. [2678438]
-
SPreCalc6 7.2.036. [1759351]
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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]
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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]
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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]
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SPreCalc6 7.3.032. [2709016]
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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