Question

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share? PLEASE HELP WILL MARK BRAINLIEST

Answer 1

Answer:

sinx = cosy = 0.6

Step-by-step explanation:

1) sinx=6/OP; cosy=6/OP;

2) The length of the side OP is 10;

3) sinx=cosy=6/10=0.6.

The relationship is sinx=cosy (and siny=cosx).

Answer 2

Answer:

Trig ratios:

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

where $\theta$ is the angle, O is the side opposite the angle, A is the side adjacent the angle, and H is the hypotenuse of a right triangle

Using Pythagoras' Theorem $a^2+b^2=c^2$ to calculate the hypotenuse OP:

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

$\implies c = \sqrt{100}=10$

$\sin(x)=\dfrac{O}{H}=\dfrac{6}{OP}=\dfrac{6}{10}$

$\cos(y)=\dfrac{A}{H}=\dfrac{6}{OP}=\dfrac{6}{10}$

$\implies \sin(x)=\cos(y)=\dfrac{6}{10}=0.6$