Trigonometric fx

When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of
angle θ : sin φ, cos φ, tan φ, cotan φ.

Correct answer:

s =  0.9487
c =  0.3162
t =  3

Step-by-step explanation:

$$\begin{gathered} P=(1,3) \\ m=\sqrt{P_x^2+P_y^2}=\sqrt{1^2+3^2}=\sqrt{10}\doteq 3.1623 \\ \sin \phi =\frac{y}{m} \\ s=\frac{P_y}{m}=\frac{3}{3.1623}=0.9487 \end{gathered}$$

$$\begin{gathered} \cos \phi =\frac{x}{m} \\ c=\frac{P_x}{m}=\frac{1}{3.1623}=0.3162 \end{gathered}$$

$$\begin{gathered} t=\frac{\sin \phi }{\cos \phi }=\frac{P_y}{P_x} \\ t=\frac{P_y}{P_x}=\frac{3}{1}=3 \end{gathered}$$

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