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Lorico [155]
1 year 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]1 year 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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Igoryamba

Answer:

S

ThenSn=n(a1+an)2Sn=n(a1 + an)2 , where nn is the number of terms, a1a1 is the first term and anan is the last term. The sum of the first nn terms of an arithmetic sequence is called an arithmetic series .

Step-by-step explanation:

4 0
2 years ago
If line GH is perpendicular to line HJ, then GJ is ____ HJ.
valentinak56 [21]

Option A: >

Solution:

Given a triangle GHJ.

The line GH is perpendicular to line HJ.

This means the triangle is a right angled triangle.

In ΔGHJ, GH is the base of the triangle and

HJ is a height of the triangle.

Then the third side must be the hypotenuse of the right triangle.

We know that by the Pythagoras theorem,

(\text {Hypotenuse})^2=(\text{Base})^2+(\text{Height})^2

(\text {GJ})^2=(\text {GH})^2+(\text {HJ})^2

This clearly shows that the hypotenuse is greater than the height.

⇒ GJ > HJ

Option A: > is the correct answer.

If line GH is perpendicular to line HJ, then GJ is > HJ.

3 0
3 years ago
What are the domain and range of this function?
Arlecino [84]

Answer:

Correct answer:  The third answer is correct

Step-by-step explanation:

The domain of each function is defined by observing the behavior of the function from left to right by following the growth of numbers on the x axis of real numbers.

In the same way, the range of each function is defined by observing the behavior of the function from the bottom y axis upwards by following the growth of numbers on the y axis of real numbers.

The given function extends from negative infinite to positive infinite on the x axis and that is the domain of this function.

The minimum of a given function is 4, which means that the function exists from 4  upwards and that is the range of the function.

Domain; all real numbers or x ∈ ( -∞ , + ∞)

Range:  ( y ≥ 4 )

God is with you!!!

8 0
3 years ago
What is the intersection of the three sets: A = {1,2,3,4,5),
Lubov Fominskaja [6]

Answer:

(2,3)

Step-by-step explanation:

The only two numbers all three share

5 0
3 years ago
A circle has a radius of 8cm. An angle of 1.4 radians is subtended at the center by an arc. Calculate the length of the arc
AURORKA [14]

Answer:

11.2 cm

Step-by-step explanation:

Given that;

Arc Length Formula (if θ is in radians): l = ϴ × r

ϴ = angle subtended in radians

r= radius of the circle

l = 8cm × 1.4 radians

l= 11.2 cm

5 0
3 years ago
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