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}}](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cfrac%7Bopposite%7D%7B%5Ctext%7Bhypotenuse%7D%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B13%7D%7D)
![\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cfrac%7Badjacent%7D%7B%5Ctext%7Bhypotenuse%7D%7D%3D%5Cfrac%7B3%7D%7B%5Csqrt%5B%5D%7B13%7D%7D)
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}})](https://tex.z-dn.net/?f=%5Csin%202x%3D2%28%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29%28%5Cfrac%7B3%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29)
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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ccos%202x%3D%28%5Cfrac%7B3%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29%5E2-%28%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%29%5E2%20%5C%5C%20%20%5C%5C%20%3D%5Cfrac%7B9%7D%7B13%7D-%5Cfrac%7B4%7D%7B13%7D%20%5C%5C%20%3D%5Cfrac%7B5%7D%7B13%7D%20%5Cend%7Bgathered%7D)
Hence, cos2x = 5/13
tan2x = 2tanx / 1- tan²x
OR
Hence, tan2x = 12/5
Therefore,
sin2x =12/13
cos2x = 5/13
tan2x = 12/5
See the picture attached.
We know:
NM // XZ
NY = transversal line
∠YXZ ≡ ∠YNM
1) <span>
We know that ∠XYZ is congruent to ∠NYM by the reflexive property.</span>
The reflexive property states that any shape is congruent to itself.
∠NYM is just a different way to call ∠XYZ using different vertexes, but the sides composing the two angles are the same.
Hence, ∠XYZ ≡ <span>∠NYM</span> by the reflexive property.
2) Δ<span>
XYZ is similar to ΔNYM by the AA (angle-angle) similarity theoremThe AA similarity theorem states that if two triangles have a pair of corresponding angles congruent, then the two triangles are similar.
Consider </span>Δ<span>XYZ and ΔNYM:
</span>∠YXZ ≡ <span>∠YNM
</span>∠XYZ ≡ ∠NYM
Hence, ΔXYZ is similar to ΔNYM by the AA similarity theorem.
1/5 is equal to the 20% of the trip and that took 45 minutes.
45minutes/20% of traveled distance = X minutes/ 100% travel distance
2.25 * 100= X
225= X
So if for the 1/5 or 20% of the trip lasted 3/4hour or 45 minutes. To complete the trop you need 225 minutes or 3 hours and 45 minutes or 3 3/4 hours.
N=-6
that the answer to the question
