Quad X
Finding values of trigonometric functions of theta if terminal 6 on the side line y = (1 / 3) and quad x 3?
I'm trying to find the six trigonometric functions (sin, cos, tan, csc, sec, cot) of theta if theta side of the terminal is on the line y = (1 / 3) x, and is in Box 3. I have no idea how to go on this resolution. Can anyone help?
First find the length of the side of the triangle formed by the right of the line and the x-axis: Find the hypotenuse 1, therefore, the Pythagorean theorem: 1 ^ 2 = x ^ 2 + (1/3x) ^ 2 = 1 x ^ 2 + 1 / 9 x ^ 2 = 10 / 9 x ^ 2 9 / 10 = x ^ 2 x = sqrt (9 / 10) = 3/sqrt (10) = (3 / 10) sqrt (10), because we want to make negative quadrant 3. X = (- 3 / 10) sqrt (10) y = 1 / 3 (- 3 / 10) sqrt (10) = (- 1 / 10) sqrt (10) sin ? = y / 1 = (-1/10) sqrt (10) cos ? = x / 1 = (-3/10) sqrt (10) tan ? = y / x = 1 / 3 CSC = ? 1 / y = -10/sqrt (10) = - Sqrt (10) sec ? = 1 / x = -10 / (3 sqrt (10)) = (-1 / 3) sqrt (10) cot ? = x / y = 3
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