Question

Match each trigonometric function with its Unit Circle definition. Note that Angle A is correctly oriented for the Unit Circle definition, its terminal side intersects the Unit Circle at the point (x, y), and neither x nor y is equal to zero.

1. y
2. x
3. y/x
4. 1/y
5. 1/x
6. x/y

a. sin A
b. csc A
c. tan A
d. sec A
e. cos A
f. cot A

Answer 1

The first diagram below shows a circle with a radius of 1 (unit circle). The circle is drawn on a Cartesian graph with (0,0) as the center of the circle.

From the second diagram, we can determine the value of sin(Θ) = y
and cos(Θ) = x

We can further deduce that
tan(Θ) = $\frac{y}{x}$
sec(Θ) = $\frac{1}{cos(Θ)}$ = $\frac{1}{x}$
cosec(Θ) = $\frac{1}{sin(Θ)}$ = $\frac{1}{y}$
cot(Θ) = $\frac{cos(Θ)}{sin(Θ)}$ = $\frac{x}{y}$

Answer 2

Answer:

The required matching is a-1, b-4, c-3, d-5, e-2, f-6.

Step-by-step explanation:

Unit Circle is circle having radius 1 units and centered at origin.

The terminal side intersects the Unit Circle at the point (x, y), and neither x nor y is equal to zero.

So, perpendicular of triangle is y, base is x and hypotenuse is 1 unit.

It a right angled triangle,

$\sin A=\frac{perpendicular}{hypotenuse}\Rightarrow \frac{y}{1}=y$

$\csc A=\frac{1}{\sin A}=\frac{1}{y}$

$\tan A=\frac{perpendicular}{base}\Rightarrow \frac{y}{x}$

$\sec A=\frac{hypotenuse}{base}=\frac{1}{x}$

$\cos A=\frac{base}{hypotenuse}=\frac{x}{1}=x$

$\cot A=\frac{1}{\tan A}=\frac{x}{y}$

Therefore the required matching is a-1, b-4, c-3, d-5, e-2, f-6.