Questions: Determine the values of the trigonometric functions of α, where sin α = 7/25, and cos α = 24/25. tan α = (Type a simplified fraction.)

Solution Steps

The tangent of an angle \( \alpha \) is defined as the ratio of the sine of \( \alpha \) to the cosine of \( \alpha \). Mathematically, this is expressed as: \[ \tan \alpha = \frac{\sin \alpha}{\cos \alpha} \]

We are given \( \sin \alpha = \frac{7}{25} \) and \( \cos \alpha = \frac{24}{25} \). Substitute these values into the tangent formula: \[ \tan \alpha = \frac{\frac{7}{25}}{\frac{24}{25}} \]

To simplify the fraction, multiply the numerator by the reciprocal of the denominator: \[ \tan \alpha = \frac{7}{25} \times \frac{25}{24} = \frac{7}{24} \]

Final Answer