Download 5-4 Sum and Difference Identities page 341 25-35 odd 41

5-4 Sum and Difference Identities
Write each trigonometric expression as an algebraic expression.
25. SOLUTION: If we let
and
, then
. Sketch one right triangle with an acute
and angle and another with an acute angle . Label the sides such that
and
. Then use the
Pythagorean Theorem to express the length of each third side.
and Using these triangles, we find that
these values in
. Substitute
and simplify.
27. SOLUTION: If we let
angle
and
, then
and another with an acute angle
and . Label the sides such that
Pythagorean Theorem to express the length of each third side.
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. Sketch one right triangle with an acute
and
. Then use the
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5-4 Sum and Difference Identities
27. SOLUTION: If we let
angle
and
, then
and another with an acute angle
and . Sketch one right triangle with an acute
. Label the sides such that
and
. Then use the
Pythagorean Theorem to express the length of each third side.
Using these triangles, we find that
. Substitute these values in
,
, and
and
simplify.
29. SOLUTION: eSolutions Manual - Powered by Cognero
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5-4 Sum and Difference Identities
29. SOLUTION: If we let
, then
. Sketch a right triangle with an acute angle . Label the sides such that
. Then use the Pythagorean Theorem to express the length of the third side.
Using this triangle, we find that
. Substitute this value in
and
simplify.
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triangle,
we find that
5-4 Using
Sum this
and
Difference
Identities
. Substitute this value in
and
simplify.
31. SOLUTION: eSolutions Manual - Powered by Cognero
If we let
, then
. Sketch a right triangle with an acute angle . Label the sides such that
. Then use the Pythagorean Theorem to express the length of the third side.
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5-4 Sum and Difference Identities
31. SOLUTION: If we let
, then
. Sketch a right triangle with an acute angle . Label the sides such that
. Then use the Pythagorean Theorem to express the length of the third side.
Using this triangle, we find that
. Substitute this value in
and
simplify.
Verify each cofunction identity using one or more difference identities.
33. sec
= csc x
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SOLUTION: Page 5
5-4 Sum and Difference Identities
Verify each cofunction identity using one or more difference identities.
33. sec
= csc x
SOLUTION: Verify each reduction identity.
– ) = – cos
35. cos (
SOLUTION: Find the solution to each expression on the interval [0, 2π).
41. cos( + x) + cos ( + x) = 1
SOLUTION: On the interval [0, 2 ),
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43. sin Manual - + sin = SOLUTION: when x =
and x =
.
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the and
interval
[0, 2 ),
when x =
5-4 On
Sum
Difference
Identities
43. sin
+ sin and x =
.
= SOLUTION: On the interval [0, 2 ),
45. tan (
+ x) + tan (
when x =
and x =
.
+ x) = 2
SOLUTION: On the interval [0, 2 ),
when x =
and x =
.
Verify each identity.
47. cot
– tan
= SOLUTION: 49. 2 sinManual
a cos- bPowered
= sin (a
+ b) + sin
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SOLUTION: (a – b)
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5-4 Sum and Difference Identities
49. 2 sin a cos b = sin (a + b) + sin (a – b)
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