sint=-4/5 find sin2t, cos2t, cos t/2, tan t/2

Question

find sin2t, cos2t, cos t/2, tan t/2 

Answer 1

sine is negative is quadrants 3 and 4

 

sine is opposite / hypotenuse ---> opposite = -4 and hypotenuse = 5

So the other leg , by pythagorean theorem, is sqrt ( 5^2 - (- 4)^2) =

                                                                    sqrt ( 25 - 16) =

                                                                    sqrt(9) = 3

 

     

Since x=3 and y = -4 we have t = inverse_sine(4/5) = 53.13.

In the 4th quadrant, the angle is 360 - 53.13 = 306.87

 

Nevertheless, In the 3rd quadrant we have 180 + 53.13 = 233.13

 

 

The follow table shows the results of the other trig expressions.

 

T1 deg 233.13
T2 deg 306.87
T1 rad 4.068886085
T2 rad 5.355891876
2*T1 8.13777217
2*T2 10.71178375
T1/2 2.034443043
T2/2 2.677945938
sin(2*T1) 0.960001
Sin(2*T1) -0.960001
cos(2*t1) -0.27999657
cos(2*t2) -0.27999657
cos(t1/2) -0.447212797
cos(t2/2) -0.89442759
tan(t1/2) -2.000004466
tan(t2/2) -0.499998883