if cos theta is 10/17 then what is sin theta

Question

I am asking about a pythagorean Trig question that I was asked in my math homework.

 

Answer 1

Hi Melissa,

 

If it is Pythagorean, then we are talking about a right triangle.

 

Remember that cos = adj/hyp and sin = opposite/hypotenuse

 

so we have a right triangle with one side equal to 10 and hypotenuse equal to 17

We can find the length of the other side according to the Pythagorean theorem

17² = 10² + x²

x = 13.75 which is the opposite side for angle theta

Since sin theta = opposite/hypotenuse then sin theta=13.75/17

 

Answer 2

From the trig. identity; Cos²X + Sin²X = 1  (I used X instead of theta for convenience sake)

 

Hence Sin²X = 1 - Cos²X; = 1 - (10/17)²

 

= 1 - 100/289 = 189/289 

 

Hence SinX =  3/17 * (21)^1/2  or 13.75/17 = 0.809