Questions: Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given point. (24,7) sin θ=7/25 cos θ=

Solution Steps

The radius \(r\) is calculated using the Pythagorean theorem: \(r = \sqrt{24^2 + 7^2} = 25\).

Using the definitions of trigonometric ratios in a right-angled triangle, we find:

• \(\sin \theta = \frac{y}{r} = 0.28\)
• \(\cos \theta = \frac{x}{r} = 0.96\)
• \( an \theta = \frac{y}{x} = 0.29\) if \(x \neq 0\).

For the reciprocal trigonometric functions, we find:

• \(\cot \theta = \frac{1}{\tan \theta} = 3.43\) if \(y \neq 0\).
• \(\sec \theta = \frac{1}{\cos \theta} = 1.04\) if \(x \neq 0\).
• \(\csc \theta = \frac{1}{\sin \theta} = 3.57\) if \(y \neq 0\).

Final Answer: