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
The answer is 2x^2 to the question
Answer:
Option D (r(t) = 3.50t +25
; r(8) = 53)
Step-by-step explanation:
The fixed cost to rent the kayak $25. This is the cost which remains fixed irrespective of the usage of the kayak. The variable cost of using the kayak is the cost which depends on the usage of the kayak. It is mentioned that the kayak is used for 4 hours and the company charges $3.5 for every half hour. The cost function is given by:
r(t) = 25 + 3.5t ; there r is the total cost of using the kayak and t is the number of half-hours the kayak is used.
4 hours means that there are 8 half-hours. Therefore, t=8. Put t=8 in r(t).
r(8) = 25 + 3.5*(8) = 25 + 28 = 53.
Therefore, Option D is the correct answer!!!
Answer:
i am pretty sure its 8
Step-by-step explanation:
because a negative plus a positive = wichever one is bighger and 8 is bigger than 3 so 11 is positive. 8 +3 = 11
So it’s A
in all the other ones we can see that the angles in the same position as x and 75 are all equal
and because the question tells us that they are all structured the same with p and f being parallel we can assume x is equal to what’s congruent to it
there is a rule that states this
cap congruent angle postulate i believe
which states that if two parallel lines are cut by a transversal, then corresponding angles are congruent
