William W. answered • 09/26/19
Experienced Tutor and Retired Engineer
The trig functions (like sine) are taken on an angle. For example we say sin(30°). So we expect that "t" must be an angle. To determine what -t is, let's figure out what t is. t is the angle that gives a sine of 0.35, To find that we use inverse sine. So look for sin-1 on your calculator and type in sin-1(.35). Make sure your calculator is set on degree mode to get an answer in degrees or set to radian mode to get an answer in radians. You'll get t = 20.5° or 0.358 radians. So -t is -20.5° or -0.358 radians.
Every time you make one complete revolution around the unit circle the values of sine and cosine start repeating. One time around the circle is 360° or 2π radians (that's 2 pi not 2 pie). So if we add 2π radians, it doesn't change the value of sine so sin(t + 2π) = sin(t) = 0.35
