All categories

3 years ago

What is helpful Problem-solving

1 answer:

6 0

Helpful problem solving is handling all problems the same , weather big , small or complex you should always problem solve in a fair way that’s convenient to everyone’s needs

You might be interested in

Find , , and if and terminates in quadrant .

ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

• cos2x

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

$\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}$ $\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}$

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

$\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})$ $=\frac{12}{13}$

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

$\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\ \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}$

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

$\tan 2x=\frac{2\tan x}{1-\tan ^2x}$ $=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}$ $=\frac{\frac{4}{3}}{1-\frac{4}{9}}$ $=\frac{\frac{4}{3}}{\frac{9-4}{9}}$ $=\frac{\frac{4}{3}}{\frac{5}{9}}$ $=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}$

$\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0

1 year ago

Help with this picture too

vodka [1.7K]

Answer:

(6x+3)(6x-3)

Step-by-step explanation:

I used FOIL

Multiply the first numbers 6x*6x=36x^2

The outer -18x

Inner 18x which the outer and the inner cross out

Last 3*-3=-9

36x^2 -9

8 0

3 years ago

Read 2 more answers

Sara’s teacher gave her class 10 quizzes, each worth 30 marks. Sara’s marks on the test are given below.

leonid [27]

Answer:

The mean is 6.6

The median is 16

mode is 18

Step-by-step explanation:

I'm not sure if this is tight but yeah:)

4 0

3 years ago

Three vertices of a square are (-2, 2), (-2, -3), and (3, -3). What is the fourth vertex of the square?

Oxana [17]

(-2,2) and (-2,-3) are the bottom vertices, since (3,-3) is the top you can tell that it is the upper left vertex since it lines up with (2,-3), so the fourth vortex would line up with (-2,2) and would therefore be C. (3,2)

5 0

3 years ago

What are not the multiples of 4

Goshia [24]

Is this multiple choice

5 0

3 years ago