The terminal side of an angle theta in standard position passes through the point (-6,-3). Use the figure to figure out the following value. Cos theta

Answer 1

Begin by plotting your point to see that the point (-6,-3) falls in the third quadrant.

Draw a right triangle so that the angle theta extends from the x-axis between quadrants II and III. The horizontal leg of the triangle, which connects (0,0) and (-6,0), will have a length of 6. The vertical leg of the triangle, which connects the points (-6,0) and (-6,-3), will have a length of 3. The hypotenuse will be a diagonal line connecting (0,0) to (-6,-3).

Use the Pythagorean Theorem to solve for the length of the hypotenuse.

a² + b² = c² , where a and b are the legs and c is the hypotenuse

3² + 6² = c²

45 = c²

^{√45 = c}

Label your drawing accordingly.

Remember that the cos θ is equal to the ratio of the adjacent side of the triangle over the hypotenuse. Therefore:

cosθ = -6 / √45 .

If you rationalize this:

cosθ = - (6√45) / 45

Simplified:

-(6*√(9*5)) / 45 = -(6* 3 √5)/45 = -(2√5) / 5

*Notice that the answer is negative because the cos of any angle that lies in the third quadrant will be negative.