Question

The angle \theta_1θ 1 ​ theta, start subscript, 1, end subscript is located in Quadrant \text{IV}IVstart text, I, V, end text, and \cos(\theta_1)=\dfrac{3}{5}cos(θ 1 ​ )= 5 3 ​ cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 3, divided by, 5, end fraction .

Answer 1

Answer:

$\sin(\theta_1)=-\dfrac{4}{5}$

Step-by-step explanation:

Given the angle $\theta_1$ located in $\text {Quadrant IV}$.

$\cos(\theta_1)=\dfrac{3}{5}$

We want to determine the value of $\sin(\theta_1)$

Now,

$\cos(\theta)=\dfrac{Adjacent}{Hypotenuse}\\ Therefore:\\Adjacent=3\\Hypotenuse=5\\Using Pythagoras theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\5^2=Opposite^2+3^2\\Opposite^2=5^2-3^2=16\\Opposite^2=4^2\\ Opposite=4$

In Quadrant IV,  x is positive, and y is negative.

Therefore, Opposite=-4

$\sin(\theta_1)=-\dfrac{4}{5}$