Find sinØ and tanØ if cosØ =-3/4 and sin Ø > 0

Question

Use the Pythagorean identities to find each function value.

Answer 1

Given Cos(∅) = -3/4

Remember "Soh Cah Toa" ? that should tell us the length of the side adjacent to angle ∅ is 3 and the hypotenuse is 4 in the right triangle.

In, Quadrant II, since the Cos (∅) is negative. (I hope you are thinking about the Unit circle!)

To find Sin (∅), we use the Pythagorean identity a²+b²=c² , where c is the hypotenuse, and it is okay to say a is the adjacent side. Substitute and solve for b.

Once we have the value for b, which is the side opposite to the angle ∅, we can find Sin(∅) =b/h

Then, substitute in tan(∅) = Sin(∅) / Cos(∅), to find tan(∅). What do you remember /know about the sign for the trig function tan ?

Please recall the sign of the Trig functions in the 4 quadrants and that will tell you the significance of why the question mentions Sin(∅) > 0.