The point P(10, 2) is on the terminal side of an angle x. Find the exact values of each trigonometric function.

To find the exact values of each trigonometric function for the angle whose terminal side passes through the point P(10, 2), we first need to determine the radius (r) of the right triangle formed by this point and the origin (0, 0).

The radius can be calculated using the Pythagorean theorem:

r = √(x² + y²)

Where x = 10 and y = 2.

Substituting the values, we get:

r = √(10² + 2²) = √(100 + 4) = √104 = 2√26.

Now that we have r, we can find the six trigonometric functions:

• Sine: sin(x) = &frac{y}{r} = &frac{2}{2√26} = &frac{1}{√26}.
• Cosine: cos(x) = &frac{x}{r} = &frac{10}{2√26} = &frac{5}{√26}.
• Tangent: tan(x) = &frac{y}{x} = &frac{2}{10} = &frac{1}{5}.
• Cosecant: csc(x) = &frac{r}{y} = &frac{2√26}{2} = √26.
• Secant: sec(x) = &frac{r}{x} = &frac{2√26}{10} = &frac{√26}{5}.
• Cotangent: cot(x) = &frac{x}{y} = &frac{10}{2} = 5.

In conclusion, the exact values of the trigonometric functions for the angle x with the terminal side passing through the point P(10, 2) are:

• sin(x) = &frac{1}{√26}
• cos(x) = &frac{5}{√26}
• tan(x) = &frac{1}{5}
• csc(x) = √26
• sec(x) = &frac{√26}{5}
• cot(x) = 5