Find the value of all six trigonometric functions for theta = -5 pi over 4

Question

Find the value of all six trigonometric functions for theta = -5 pi over 4

Answer 1

If you work more comfortably in degrees, recall that 2 pi radii make up the circumference of a circle; hence, 2pi=360deg.

 

So given pi=180 deg, what quadrant must -5pi/4 be in?

 

If you are comfortable in radians, you can perhaps answer this directly.  More importantly, what is the reference angle of this angle?  (i.e. what is the angle measurement between this angle and the horizontal axis?)

 

Then trig function of this angle will simply be trig function of the reference angle (other than a possible sign change)...in other words, the abs val of a trig function value of an angle is equal to that of its reference angle.

 

The way the signs can be determined is by recognizing that among the three trig functions sin, cos, and tan, those that are positive in the 4 quadrants are : I: ALL, II: SIN, III: TAN, IV: COS.

 

The reciprocal trig functions of sin, cos, and tan (or csc, sec, and cot respectively) can be found fairly simply once you determine the value of the trig functions.

 

The value of the sin and cos can be determined knowing the ratios in "special" triangles; tan=sin/cos.

 

Hope this helps for this problems and beyond.