What is cos θ if sin θ = −8/10 and θ is in Quadrant III?

Answer 1

Hi Sylvia,

Drawing out the quadrants cos of an angle is negative in the third quadrant. Your drawing should indicate that x and y are negative. Then since we are working with a right triangle, again your diagram should indicate that. Determine the value of the third side. You know one is - 6 and the other opposite the 90 degree angle, the hypotenuse is 10.

cos of an angle is adjacent divided by the hypotenuse.

I hope this helps. If not,, please tell me.

Mona

Answer 2

cosine is negative in Quadrant III.

Use a pythagorean theorem to find the other leg. a² = c² - b²

adjacent leg = √(10² - 8²)

cos θ = -6/10