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Given Sin(theta)= -.487 and 3pi/2 < theta < 2pi, find the Exact Value of theta in degrees as well as in radians accurate to three decimal units. SHOW ALL WORK! Then, find Cos theta and Tan theta.


Answer before 10:30pm PST for 20 points!

Respuesta :

calculista

We know that

if 3pi/2 < theta < 2pi

then

theta belongs to the IV quadrant

so, 

sin (theta) is negative

cos (theta) is positive

tan (theta) is negative

step 1, 

Find the value of theta

sin (theta) = -.487

theta =arc sin (0.487)-------------> theta=29.144 degrees

remember that theta belongs to the IV quadrant

so

theta=360° - 29.144--------> theta=330.856°

Convert to radians

pi radians---------> 180°

x------------------------> 330.856°

x=1.838pi radians

the answer to part a) is

theta is 330.856°

the answer to part b) is

theta is 1.838pi radians

step 2

find the value of cos theta

remember that cos theta is positive

cos²theta+sin²theta=1

cos²theta=1-sin²theta----------> cos ²theta=1-(-0.487)²

cos²theta=0.762831

cos(theta)=0.873

the answer to part c) is

cos (theta) =0.873

step 3

find the value of tan theta

tan (theta) =sin theta/cos theta

so

tan(theta)=(-0.487)/(0.873)-------------> tan theta=-0.558

the answer to Part d) is

tan (theta) = -0.558


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