Question

question #15 the point (7, - 24) is on the terminal side of an angle in standard position. find the exact value of the trig function of the angle. find tanθ. -24/7 -25/7 -7/25 -7/24 question #16 determine the angle or angles on the unit circle that have a tangent ratio of 1. θ = 0° and θ = 360° θ = 135° and θ = 315° θ = 90° and θ = 270° θ = 45° and θ = 225°

Explanation:

Step1: Recall tangent - ratio formula

For an angle $\theta$ in standard position with a point $(x,y)$ on its terminal side, $\tan\theta=\frac{y}{x}$.

Step2: Identify $x$ and $y$ values

Given the point $(7, - 24)$, we have $x = 7$ and $y=-24$.

Step3: Calculate $\tan\theta$

$\tan\theta=\frac{y}{x}=\frac{-24}{7}=-\frac{24}{7}$.

for Question #16:
Recall that $\tan\theta=\frac{\sin\theta}{\cos\theta}$. We want $\tan\theta = 1$, so $\frac{\sin\theta}{\cos\theta}=1$, which means $\sin\theta=\cos\theta$.
On the unit - circle, $\sin\theta = y$ and $\cos\theta=x$. The points where $x = y$ are $(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ and $(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$.
The angles corresponding to these points are $\theta = 45^{\circ}$ (or $\frac{\pi}{4}$ radians) and $\theta = 225^{\circ}$ (or $\frac{5\pi}{4}$ radians).

Answer:

A. $-\frac{24}{7}$