Question

The terminal side of an angle in standard form passes through the point (6, -4). Find the following function values:

A) sin(θ) = -2/5, cos(θ) = 6/5, tan(θ) = -3/2.
B) sin(θ) = 3/5, cos(θ) = 4/5, tan(θ) = 3/4.
C) sin(θ) = 4/5, cos(θ) = 3/5, tan(θ) = 4/3.
D) sin(θ) = -3/5, cos(θ) = 4/5, tan(θ) = -3/4.

Answer 1

The trigonometric function values for an angle whose terminal side passes through (6, -4) should be derived using the coordinates and the Pythagorean theorem. Since none of the provided options match these calculated values, all options A, B, C, and D are incorrect.

Step-by-step explanation:

The student's question involves determining the trigonometric function values for an angle θ whose terminal side passes through the point (6, -4).

In this context, the answers represent the sine (sin), cosine (cos), and tangent (tan) of the angle. To find these values, one should note that for an angle in standard position:

• The cosine (cos) of the angle is the x-coordinate divided by the hypotenuse.
• The sine (sin) of the angle is the y-coordinate divided by the hypotenuse.
• The tangent (tan) of the angle is the y-coordinate divided by the x-coordinate.

The hypotenuse (h) can be found using the Pythagorean theorem: √(x² + y²).

For the point (6, -4), the hypotenuse is √(6² + (-4)²) = √(36 + 16) = √52. Therefore, the correct trigonometric function values are:

• sin(θ) = -4/√52
• cos(θ) = 6/√52
• tan(θ) = -4/6 = -2/3

After simplifying, we get:

• sin(θ) = -4/(√52)
• cos(θ) = 6/(√52)
• tan(θ) = -2/3

These values should be rationalized by multiplying the numerator and denominator by √52 if necessary. Given the options provided by the student, none of them correctly represent the sin, cos, and tan values for the point (6, -4) based on the hypotenuse calculation. Therefore, all options A, B, C, and D are incorrect.