The identity Sin(α)/Tan(α) = Cos(α) is valid
Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
Lets prove this identity by proceeding with the LHS
= Sin(α)/Tan(α)
= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))
= Sin(α)xCos(α) / Sin(α)
= Cos(α)
Hence verified
Learn more about Trigonometric Ratios here :
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Answer:
He will need 8.34 yards of fabric.
Step-by-step explanation:
Given that,
The length of the fabric, l = 2 2/3 yards = 8/3 yards
The width of the fabric, b = 1 1/2 yards = 3/2 yards
We need to find the piece of fabric Roberto needs. It is equal to the perimeter of the fabric such that,
So, he will need 8.34 yards of fabric.
<span>Pick two pairs: 4x - 3y + z = - 10. 2x + y + 3z = 0. ... Eliminate the same variable from each system: 4x - 3y + z = - 10. 2x + y + 3z = 0. ... Solve the system of the two new equations: -5y - 5z = - 10. 5y - 7z = 34. ... Substitute into one of the original equations: - x + 2y - 5z = 17. ... <span>Check: Does 2(1) + 4 + 3(- 2) = 0 ? Yes.</span></span>
The answer is
A. D<span>O, 0.75</span> (x,y) = (0.75x, 0.75y<span>)
B. </span>LM<span> is parallel to </span>L'M'<span>.
and C. </span><span>The vertices of the image are closer to the origin than those of the pre-image.</span>
Answer:
Metallic Balloons = 74
Bunches of Helium Balloons = 38
Step-by-step explanation:
The question basically asks for the number of "metallic balloons" sold and the number of bunches of "helium balloons" sold.
We will do it in our way. Let B be number o metallic balloons and H be number of bunches of Helium balloons.
Since Metallics cost 2 each and Heliums cost 3.5 per bunch and totaled sales is 281, we can write and equation as:
2B + 3.5H = 281
and, since they sold 36 MORE metallic than helium ,we can write an equation as:
B - 36 = H
We can put 2nd equation in 1st one and solve for B first:
B = 74
Now, we find H:
H = B - 36
H = 74 - 36 = 38
H = 38
