Intro to Vector Mathmatics : Trigonometric Graphs, The Unit Circle



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Current Score : – / 115 Due : Sunday, February 7 2016 10:00 PM GST
1. –/8.33 pointsSPreCalcINT6 7.1.004.
Write the trigonometric expression in terms of sine and cosine, and then simplify.
2. –/8.33 pointsSPreCalcINT6 7.1.016.
Simplify the trigonometric expression.
3. –/8.33 pointsSPreCalcINT6 7.1.022.
Simplify the trigonometric expression.
HW1 (Homework)
Hamad Al Derei
:HE$VVLJQ
cos t csc t
cot x
csc(−x)
cot x sin x sec x


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4. –/8.33 pointsSPreCalcINT6 7.1.028.
Consider the given equation.
(a) Verify algebraically that the equation is an identity.
This answer has not been graded yet.
(b) Confirm graphically that the equation is an identity.
This answer has not been graded yet.
5. –/8.33 pointsSPreCalcINT6 7.1.036.
Verify the identity.
Use the Even­Odd Identities to rewrite the expression.
Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine.
Use a Pythagorean Identity to rewrite the expression in terms of a single function, and then simplify.
cot y = csc y − sin y
sec y
cos(−Ƚ) cot(−Ƚ) + sin(−Ƚ) = −csc Ƚ
cos(−Ƚ) cot(−Ƚ) + sin(−Ƚ) =
− sin Ƚ
= − cos Ƚ − sin Ƚ
=
sin Ƚ
sin Ƚ
= =
sin Ƚ


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6. –/8.33 pointsSPreCalcINT6 7.1.048.
Verify the identity.
Expand the product.
Use the Reciprocal Identities, and then simplify.
Use a Pythagorean Identity, and then simplify.
(cot x − csc x)(cos x + 1) = −sin x
(cot x − csc x)(cos x + 1) =
cot x cos x + cot x − csc x cos x −
=
+ − −
=
cos2 x
sin x
cos x
sin x
cos x
sin x
sin x
= =
sin x


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7. –/8.33 pointsSPreCalcINT6 7.1.052.
Verify the identity.
Use a Pythagorean Identity, and then simplify.
8. –/8.33 pointsSPreCalcINT6 7.1.058.
Verify the identity.
Multiply the numerator and denominator by a common value, and then simplify.
Use a Pythagorean Identity.
2 sin2 x − 1 = 1 − 2 cos2 x
2 sin2 x − 1 =
2
− 1
=
2 −
− 1
=
=
cos x + 1
cos x − 1
−sin2 x
(cos x − 1)2
= =
cos x + 1
cos x − 1
cos x + 1
cos x − 1
cos x − 1
(cos x − 1)2
=


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9. –/8.33 pointsSPreCalcINT6 7.1.069.
Verify the identity.
Use the Reciprocal Identities, and simplify the compound fraction.
cot x − csc x = cot x
1 − sec x
= = = = =
cot x − csc x
1 − sec x
−
1 −
cos x
sin x
1
sin x
1
cos x
−
1 −
cos x
sin x
1
sin x
1
cos x
sin x cos x
cos x
sin x (cos x − 1)
sin x


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10.–/8.33 pointsSPreCalcINT6 7.1.078.
Verify the identity.
Use the Pythagorean and Reciprocal Identities to simplify.
11.–/8.33 pointsSPreCalcINT6 7.1.082.
Verify the identity.
This answer has not been graded yet.
sin2 t + cot2 t − 1 = cot2 t
cos2 t
= =
+
=
+
=
+ csc2 t
=
sin2 t + cot2 t − 1
cos2 t
+ cot2 t
cos2 t
1
cos2 t
cos2 t
sin2 t
1
cos2 t
1
sin2 t
cot2 x − tan2 x = csc2 x − sec2 x


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12.–/8.37 pointsSPreCalcINT6 7.1.092.
Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7). Assume that
13.–/1 pointsSPreCalcINT6 7.2.004.
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
14.–/1 pointsSPreCalcINT6 7.2.010.
Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1.
15.–/2 pointsSPreCalcINT6 7.2.015.
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.
Find its exact value.
0 ≤ Ʌ < Ɏ/2.
1 + x2, x = tan Ʌ
sin 255°
cos 17Ɏ
12
sin 14° cos 16° + cos 14° sin 16°


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16.–/1 pointsSPreCalcINT6 7.2.026.
Prove the identity.
This answer has not been graded yet.
17.–/5 pointsSPreCalcINT6 7.2.021.
Prove the cofunction identity using the Addition and Subtraction Formulas.
Since is undefined, use a Reciprocal Identity, and then use the Substitution Formulas to simplify.
cos x − Ɏ = sin x
2
tan Ɏ − u = cot u
2
tan Ɏ
2
tan − u =
= = = =
Ɏ2
sin
cos Ɏ − u
2
cos u − cos sin u
cos cos u + sin sin u
Ɏ2
Ɏ2
Ɏ2
cos u − 0 sin u
0 cos u + 1 sin u
sin u


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18.–/1 pointsSPreCalcINT6 7.2.046.
Write the given expression in terms of x and y only.
19.–/1 pointsSPreCalcINT6 7.2.054.
Evaluate the expression under the given conditions.
tan(Ʌ + ;)ߖɅ in Quadrant III, sin ߖ ߖin Quadrant II
20.–/1 pointsSPreCalcINT6 7.2.057.
Write the expression in terms of sine only.
sin(sin−1 x + cos−1 y)
cos Ʌ = − 1 ,
3 = ,
12
3 sin 4Ɏx + 3 3 cos 4Ɏx


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21.–/2 pointsSPreCalcINT6 7.2.060.
Consider the following equation.
(a) Express the function in terms of sine only.
(b) Graph the function.
f(
x) = sin x + cos x
f(
x) =
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