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Rosemary Spencer
Mathematics
10 October, 06:49
If cos θ=-8/17, and 180°θ<270°, what is sin θ?
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Susan
10 October, 07:00
0
-15/17
Step-by-step explanation:
One method is to use Pythagorean identity.
sin² θ + cos² θ = 1
sin² θ + (-8/17) ² = 1
sin² θ + 64/289 = 1
sin² θ = 225/289
sin θ = ±15/17
Since θ is in the third quadrant, sin θ < 0. So sin θ = - 15/17.
Another method is to draw a triangle in the third quadrant, with angle θ, adjacent side - 8, and hypotenuse 17. Use Pythagorean theorem to find the opposite side:
c² = a² + b²
17² = (-8) ² + b²
b = - 15
Therefore, sin θ = - 15/17
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