rock.freak667 said:tan(t)=Opposite/Adjacent. Draw a right-angled triangle with the side opposite to the angle ,t, as x and the adjacent side to it as a. Then use pythagoras' theorem.
TristanH said:I just figured this out on my own. For anyone who is curious:
tan(t) = x/a means the opposite and adjacent legs of a right triangle with angle t, are x and a respectively. By the Pythagorean Therom, this implies that the hypotenuse is sqrt(a^2 + x^2). Since sin t = opp/hyp, sin t = x/sqrt( a^2 + x^2). QED
The formula for converting from tangent to sine is sin(t) = x/sqrt( a^2 + x^2). This formula is used to find the value of sine when given a tangent value and the length of the adjacent side (x) and the hypotenuse (a).
This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (a) is equal to the sum of the squares of the lengths of the other two sides. By rearranging the formula to solve for sine, we get sin(t) = x/sqrt( a^2 + x^2).
Sine and tangent can have values ranging from -1 to 1. These values represent the ratio of the opposite side to the hypotenuse in a right triangle, with -1 representing a negative angle and 1 representing a positive angle.
Yes, this formula is only applicable to right triangles. The tangent and sine ratios are defined specifically for right triangles, where one angle is equal to 90 degrees.
Yes, this formula can be used to find the values of other trigonometric functions such as cosine and secant. By rearranging the formula and using the Pythagorean identity (1 + tan^2(t) = sec^2(t)), we can derive the formulas for these functions as well.