If sin is 3/11 what are the other trig functions?

Answer 1

sin²(x) + cos²(x) = 1

(3/11)² + cos²(x) = 1

cos²(x) = 1 - 9/121

cos²(x) = 112/121

cos(x) = ±√(112/121) = ±4√(7)/11

The sine is positive in quadrants I and II. The cosine is positive in quadrant I and negative in quadrant II. Since we don't know the quadrant, cos(x) could be either 4√(7)/11 or -4√(7)/11.

Now that you know both the sine and cosine, the other functions are:

tan(x) - sin(x)/cos(x)

cot(x) = cos(x)/sin(x)

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

You'll get two values for each, one for the positive cosine and one for the negative cosine. If your problem tells you if its quadrant I or II, you can use only the one appropriate value for that quadrant.

Answer 2

Use the Theorem of Pythagoras to get the other leg=4√7 and make a figure...so cos = 4√7/11 and tan = (3/28)√7. You can get the other 3 functions.