The point (16, 12) lies on the terminal side of an angle. find cos, tan, and sin

1 answer:

8 0

The terminal side means that it's 16 to the right and 12 up. Which means that the triangle made from this has the sides of 16 and 12 and the hypotenuse is 20 units long. Theta, in this case, would have 16 as it's adjacent and 12 as it's opposite.
Therefore, using the Pythagorean identities:
 $sin(\theta) = \frac{12}{20} = \boxed{\frac{3}{5}} \\\ cos(\theta) = \frac{16}{20} = \boxed{\frac{4}{5}} \\\ tan(\theta) = \frac{12}{16} = \boxed{\frac{3}{4}}$

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Answer:

$0.2$ miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.

Step-by-step explanation:

As there is no graph mentioned here but the information are quite sufficient to answer the question.

We have points $(0,3), (5,4),(10,5)...$

From these points we can find the slope of the line .

From point slope formula $y-y_1=m(x-x_1)$

And assigning $(x,y) (0,3)$ and $(x_1,y_1) (5,4)$

$m=\frac{y_1-y}{x_1-x} =\frac{4-3}{5-0} =\frac{1}{5}=0.2$

This slope is also the speed of the bird which is $0.2\ miles\ per\ minute.$

As by plugging the values of any coordinate point we can confirm this.

Lets put $(10,5)$ , y-axis is the distance so in $10$ minutes the the distance covered by the bird must be equal to to y-axis value which is $5$ miles.