Sin (theta) = -4/5; Cos (theta) = 3/5; Tan (theta) = -4/3. I need to know how to get (theta) or the degrees.. the answer is 306.9 degrees but I need to know the steps.. thank you for the help!
2007-08-02 14:26:21 · 4 answers · asked by izzie 1 in Science & Mathematics ➔ Mathematics
Draw the triangles that fit the picture/problem.
this is a 3/4/5 triangle.
along the x-axis go +3 and -3
along the y-axis go +4 and -4
hypotenuese is 5.
sin(theta) = -4/5 is in quadrant 3 and 4 since y= -4
cos(theta) = 3/5 is in quadrant 1 and 4 since x= +3
tan(theta) = -4/3 is in quadrant 2 and 4 since x= -3 (Q2) or y= -4 (Q4)
theta in quadrant 4 satisfies all 3, so theta is 53.1 degrees below the x-axis in quadrant 4 (-53.1). since 0 aka 360 degrees is the positive x-axis, you can subtract 53.1 from 360.
306.9 degrees is the answer for 0<= theta <= 360
2007-08-02 20:13:49 · answer #1 · answered by wilmer 5 · 0⤊ 0⤋
Sin (theta) = -4/5 means it is in the third or fourth quadrant. Cos (theta) = 3/5 means it is in the first or the fourth quadrant.
Combining the two gives that theta must be in the fourth quadrant.
Therefore,
theta = 360 + arcsin(-4/5) = 306.87 deg
2007-08-02 21:33:06 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋
tan theta = sin theta/cos theta = (-4/5)/(3/5) = -4/3
theta = arctan (-4/3) = -53.13degrees = 360- 53.13 = 306.87 degrees = 306. 9 degrees
2007-08-02 21:37:31 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
use the inverse cos, tan, and sin on your calculator (scientific or graphing)
2007-08-02 21:29:36 · answer #4 · answered by CHLOE 2 · 0⤊ 0⤋