Verified answer

Let's interpret the information. In order for the cos Θ to be positive and tan Θ to be negative, the angle must lie in the fourth quadrant.

Therefore, the sin Θ is negative

There are many ways to get the values of the trigonometric functions now that you know this.

Draw a triangle in the 4th Quadrant with sides of 0.8 and (- 0.6) and a hypotenuse of 1

cos Θ = 0.8

sin Θ = (- 0.6)

tan Θ = (- 0.75)

QED

θ is in the 4th quadrant. So,

sinθ = -sqrt(1-0.8^2) = -0.6

tanθ = sinθ/cosθ = -0.6/0.8 = -3/4 = -0.75

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Ideas: cosθ= 0.8 & tanθ<0 means x is positive, and y is negative.

θ is in the 4th quadrant. So,

sinθ = -sqrt(1-0.8^2) = -0.6