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Lorico [155]
2 years ago
12

Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer.

round terms to three
Mathematics
1 answer:
kykrilka [37]2 years ago
8 0

Solutions of the equation are 22.5°, 30°.

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)

=2cos4θsinθ  [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = 90/4

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = 1/2

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

For more information about trigonometric identities, visit

brainly.com/question/24496175

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1/2 of 30= 1/4 of [  ]
MaRussiya [10]

Answer:

60

Step-by-step explanation:

half of 30 is 15

and 15 is 1 quarter of 60

7 0
3 years ago
The circle below has center O, and its radius is 4 ft. Given that m ZAOB=50°find the length of the minor arc AB.
exis [7]

Answer:

The length of minor arc AB is \frac{10}{9} π  ft

Step-by-step explanation:

The formula of the length of an arc in a circle is L = \frac{\alpha }{360} × 2πr, where α is the central angle subtended by the arc, and r is the radius of the circle

∵ The radius of the circle is 4 ft

∴ r = 4

∵ ∠AOB is a central angle subtended by minor arc AB

∵ m∠AOB = 50°

∴ α = 50°

Substitute the values of r and α in the rule above

∵ L = \frac{50}{360} × 2π(4)

∴ L = \frac{10}{9} π

∴ The length of minor arc AB is \frac{10}{9} π  ft

7 0
3 years ago
Find the missing angle. Round to the nearest tenth.
Paladinen [302]

Answer:

40

Step-by-step explanation:

here is a trig calculator

http://www.carbidedepot.com/formulas-trigright.asp

4 0
2 years ago
In the figure below what is the value of x?
vazorg [7]

Answer:

The value of x is 106

Step-by-step explanation:

Let us solve the question

In the given figure

∵ The triangle in the given figure has two sides equal

→ That means the triangle is an isosceles triangle

∴ The triangle is isosceles

∵ In the isosceles triangle, the base angles are equal in measures

∵ The measure of one base angle is 37°

∴ The measure of other base angle is 37°

→ The sum of the measures of the interior angles of a Δ is 180°

∵ 37° + 37° + x = 180°

→ Add the like terms

∴ 74° + x = 180°

→ Subtract 74 from both sides

∵ 74 - 74 + x = 180 - 74

∴ x = 106

∴ The value of x is 106

7 0
3 years ago
How do I figure this out?
Gnoma [55]
Staircase one looks like our normal staircase we have today which looks like it’s easier so staircase two is more difficult to walk up?

But also

staircase one will be harder because it’s just smaller? Shorter and less space for your feet to step on. Staircase two has 1 ft of space for your feet to land on and is a bit higher which seems like normal stairs? But if I go measure my staircase... I don’t think it’s 1 ft... so? Maybe it’s staircase one? I’m sorry if I’m confusing you!!

I don’t think that’s a right or wrong question? Maybe it’s just your opinion? I’m so sorry, I honestly have no clue
7 0
3 years ago
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