What is the value of sinθ given that (-6, -8) is a point on the terminal side of θ?

Solution:

Consider a = -8 and b = -6

a = opposite side of θ and b = adjacent side of θ

Using the Pythagoras theorem of triangle, let us find the hypotenuse.

r² = a² + b²

r = √(a² + b²)

Substituting the values

r = √[(-8)² + (-6)²]

r = √(64 + 36)

r = √100

r = 10

Using the trigonometric ratios

sinθ = opposite side/hypotenuse = a/r

Substituting the values

sinθ = -8/10

sinθ = -4/5

Therefore, the value of sinθ is -4/5.

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What is the value of sinθ given that (-6, -8) is a point on the terminal side of θ?

Summary:

The value of sinθ given that (-6, -8) is a point on the terminal side of θ is -4/5.