Half angles

[~Jacqueline~]

Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the Half Angle formulas.
Cos u= 3/5 0<u<pi/2



I know that the question gives the cos, the only thing I don't understand is why cos doesn't equal to anything on the unit circle so I can't put an exact answer?

 

[wjm11]

Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the Half Angle formulas.
Cos u= 3/5 0<u<pi/2

I know that the question gives the cos, the only thing I don't understand is why cos doesn't equal to anything on the unit circle so I can't put an exact answer?

The unit circle is a handy thing to have memorized, but don’t let it limit your thinking. In Trigonometry, you are not constrained to just unit circles.

Since you know “0<u<pi/2”, start by drawing a triangle in the first quadrant. You also know that “Cos u= 3/5”. Since cosine equals adjacent/hyp., label the base of your triangle as “3” and the hypotenuse as “5”.

You can now use the Pythagorean Theorem to find that the opposite side is length “4”. (It’s also handy to memorize the 3-4-5 right triangle for quick recognition.)

Finally, you have all three sides of the triangle, so you can find the values of any of the six trigonometric functions.

 

[~Jacqueline~]

Thanks! I thought that would be too easy to solve the problem! yay !