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2 years ago

Simplify the trigonometric expression sin(4x) +2 sin(2x) using Double-Angle Identities.

Mathematics

1 answer:

emmasim [6.3K]2 years ago

6 0

Answer:

8sin(x)cos³(x)

Step-by-step explanation:

sin(4x) +2 sin(2x) = 2sin(2x)*cos(2x) + 2sin(2x) = 2sin(2x)(cos2x + 1)=

= 2sin(2x)(cos²x - sin²x + cos²x + sin²x)=²2sin(2x)*(2cos²x)=

= 4*2sin(x)*cos(x)*cos²(x)= 8sin(x)cos³(x)

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A palm tree is supported by two guy wires as shown in the diagram below. Which trig expression can be used to find the height on

Volgvan

Answer:

D. $tan(30^\circ+45^\circ)$ is the correct answer.

Step-by-step explanation:

The given situation can be represented as a figure attached in answer area.

B is the base of tree.

C is the base of wires.

A and D are the end of 2 wires supporting the tree.

$\angle DCB =45^\circ\\\angle ACB =75^\circ\\$

Here, we need to find the Height of the tree which is represented the by side AB.

and we are given that bases of wires and tree base are at a distance 4 ft.

i.e. side BC = 4 ft

If we look at the $\triangle ABC$ , we are given the base BC and the $\angle ACB$ , and the perpendicular is to be find out.

We can use trigonometric identity:

$tan\theta =\dfrac{Perpendicular}{Base}$

$tan 75^\circ = \dfrac{AB}{BC}\\\bold {tan (45+30)^\circ }= \dfrac{AB}{4}\\\Rightarrow AB = \bold {tan (45+30)^\circ } \times 4 = 14.93\ ft$

Hence, D. $tan(30^\circ+45^\circ)$ is the correct answer.

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2 years ago

The populations and land areas of four cities in Texas are shown. Which statements are true? Check all that apply. The populatio

galben [10]

Im pretty sure its A, D, and E

7 0

3 years ago

Read 2 more answers

The distance a car has traveled can be represented by the equation d = 1.4m, where d represents the distance in miles and m repr

ValentinkaMS [17]

Answer:

It is the velocity of the car, the speed.

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3 years ago

Find the diameter of Oo. A line that appears to be tangent is tangent. If your answer is not a whole

Trava [24]

Answer:

Diameter = 9

Step-by-step explanation:

Let the diameter be represented as x.

Based on the secant-tangent theorem, the following equation representing the relationship between the segments would be:

(16 + x)(16) = 20²

256 + 16x = 400

Subtract 256 from each side

16x = 400 - 256

16x = 144

Divide both sides by 16

x = 144/16

x = 9

Diameter = 9

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2 years ago

What is the value of the x variable in the solution to the following system of equations?

harkovskaia [24]

Its A. x=4

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3 years ago