Question

The point (9, 12) is on the terminal side of an angle in standard position.

What is r?

A 21
B 12
C 9
D 15
E 22
F 17



What is the sine of the angle?

A 0.75
B 0.9
C 0.6
D 0.8
E 1.34
F 0.67



What is the cosine of the angle?

A 0.57
B 0.8
C 1.34
D 0.76
E 0.6
F 0.75



What is the tangent of the angle?

A 0.6
B 0.57
C 0.8
D 1.33
E 0.67
F 1.75



What is the angle?

A 44.13°
B 77.13°
C 36.87°
D 13.87°
E 53.13°
F 63.87°

Answer 1

Answer:D

Step-by-step explanation:

Answer 2

1. The value of r is 15.

2. The sine of the angle is 0.8.

3. The cosine of the angle is 0.6.

4. The tangent of the angle is
`\((4)/(3)\)` or approximately 1.33.

5. The angle is 36.87°.

Step-by-step explanation:

To determine r in the Cartesian coordinate system, we use the Pythagorean theorem,
`\( r^2 = x^2 + y^2 \)`. Given the point (9, 12),
`\( r^2 = 9^2 + 12^2 \)`. Calculating this,
`\( r^2 = 81 + 144 \)`, and
`\( r^2 = 225 \).` Taking the square root of both sides,
`\( r = √(225) = 15 \).` Therefore, the value of r is 15.

The sine of an angle in standard position is defined as
`\( \sin(\theta) = (y)/(r) \)`. In this case,
`\( \sin(\theta) = (12)/(15) = 0.8 \).`

The cosine of an angle is defined as
`\( \cos(\theta) = (x)/(r) \)`. In this instance,
`\( \cos(\theta) = (9)/(15) = 0.6 \).`

The tangent of an angle is given by
`\( \tan(\theta) = (y)/(x) \)`. For this point,
`\( \tan(\theta) = (12)/(9) = (4)/(3) \)`, which is approximately 1.33.

Finally, to find the angle
`\( \theta \)`, we use the arctangent function:
`\( \theta = \arctan\left((y)/(x)\right) = \arctan\left((12)/(9)\right) \)`. Calculating this, we find
`\( \theta \approx 36.87° \)`. Therefore, the angle is approximately 36.87°.