Question

Use the given information to determine the exact trigonometric value.

Answer 1

Answer:
`\bold{a.\quad -(2√(6))/(5)}`

Explanation:

`sin\theta=(y)/(h)\implies y=-1, h=5\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2 + y^2 = h^2\\x^2 + (-1)^2=5^2\\x^2+1=25\\x^2=24\\x=√(24)\\x=2√(6)`

`\text{Since }\theta\text{ is between }\pi\text{ and }(3\pi)/(2) \text{ (Quadrant III)},\text{ then x and y are negative.}\\\implies x=-2√(6)\\\\\\cos\theta = (x)/(h)\quad =\boxed{-(2√(6))/(5)}`