3 years ago

Help please thank you!!!

Mathematics

1 answer:

AysviL [449]3 years ago

4 0

Answer:

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Step-by-step explanation:

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Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of si

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Answer:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

To find sin x and cos y, we must first find the length of the hypotenuse (PO) of the given right triangle.

To do this, use Pythagoras' Theorem:

$a^2+b^2=c^2 \quad \textsf{(where a and b are the legs, and c is the hypotenuse)}$

Given:

a = 6
b = 8
c = PO

$\implies 6^2+8^2=PO^2$

$\implies PO^2=100$

$\implies PO=\sqrt{100}$

$\implies PO=10$

Using the found value of the hypotenuse and the trig ratios quoted above:

$\implies \sf \sin(x)=\dfrac{6}{10}=\dfrac{3}{5}$

$\implies \sf \cos(y)=\dfrac{6}{10}=\dfrac{3}{5}$

Therefore, $\sf \sin(x)=\cos(y)$

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