Question

The legs of a right triangle measure 5 inches and 7 inches. If θ is the angle between the 5-inch leg and the hypotenuse, cosθ = _____.

Answer 1

Draw the picture, use the Pythagorean Theorem to find the hypotenuse, then substitute into the definition of cos and simplify.

Answer 2

After simplification, I think the answer will look like\[\cos \theta = \frac{5 \sqrt{74} }{74}\]

Answer 3

Thanks! .58

Answer 4

No sweat. Do math every day.

Answer 5

Oh wait, question.... "There are values of t so that sin t = .3 and cos t = -.6." Is that true or false?

Answer 6

I wouldn't think so. This is another Pythagorean Theorem problem. Remember, if the hypotenuse is one (as on the unit circle; you might or might not have studied that yet)\[\cos^2 t+\sin^2t=1\]This is true always. Since you have possible values of cos and sin, you can plug it in and check. I'm pretty certain they won't work.

Answer 7

Gotcha! okay, that makes sense.