Question

Determine the quadrant of the angle’s terminal line lies Sin x = -0.45 & cos x < 0 ?

Answer 1

The angle lies in quadrant 3 .

Explanation:

`sin x = - 0.45`

Because `sinx` is negative, angle (arc) `x` lies either in Q3 or Q4.

Because `cos x < 0`, `x` lies in Q. 3.

Note:
Calculator gives 2 values of x:
`x = - 26.74^@` and
`x = 180 - (-26.74) = 180 + 26.74 = 206.74^@`
`x = 206.74^@` is the answer.

`x` lies in Quadrant 3, and
`cos (206.74)` is negative.