Question

1. (-4, -3)
2. (1, -8)
3. (-8, 15)

find the exact value of each trig defined. if not defined, write un

1. sin(π/2)
2. cot(-180°)
3. cos(-270°)
4. tan(π)

sketch each angle. then find its r

1. 135°

18.

Explanation:

Step1: Recall unit - circle values

The sine function of an angle $\theta$ on the unit - circle is given by the $y$ - coordinate of the point on the unit - circle corresponding to $\theta$. For $\theta=\frac{\pi}{2}$, the point on the unit - circle is $(0,1)$. So, $\sin\frac{\pi}{2}=1$.

Step2: Recall cotangent definition

The cotangent function is defined as $\cot\theta=\frac{\cos\theta}{\sin\theta}$. For $\theta = - 180^{\circ}=-\pi$ radians, $\cos(-\pi)=-1$ and $\sin(-\pi)=0$. Since division by zero is undefined, $\cot(-180^{\circ})$ is undefined.

Step3: Recall cosine properties

The cosine function has the property $\cos(-\alpha)=\cos\alpha$. So, $\cos(-270^{\circ})=\cos270^{\circ}$. On the unit - circle, for $\theta = 270^{\circ}$, the $x$ - coordinate (which is $\cos\theta$) is $0$. So, $\cos(-270^{\circ}) = 0$.

Step4: Recall tangent definition

The tangent function is defined as $\tan\theta=\frac{\sin\theta}{\cos\theta}$. For $\theta=\pi$, $\sin\pi = 0$ and $\cos\pi=-1$. Then $\tan\pi=\frac{0}{-1}=0$.

Answer:

1. $1$
2. undefined
3. $0$
4. $0$