SOLUTION: A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. The point P is Upper P left parenthesis Sta

Question 1037215: A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. The point P is Upper P left parenthesis StartFraction 15 Over 17 EndFraction comma eight seventeenths right parenthesisP
(15/17,8/17)
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!



The length t is the length of the red arc.

Draw a perpendicular from the point  to the
x-axis. Label it Q, and label the origin O. Then draw the radius OP.
The radius of the unit circle is 1. {In green below].

  

In geometry, you learned that a central angle is measured by the
arc it subtends.  So the central angle is also measured t.

Triangle OPQ is a right triangle. 
The side opposite angle t is PQ.
Also PQ is the y-coordinate of P, so PQ = 8/17.
The side adjacent to angle t is OQ.
Also OQ is the x-coordinate of P, so OQ = 15/17.
The radius OP is the hypotenuse, so OP = 1.


 <-- the y-coordinate of P
 <-- the x-coordinate of P





Edwin

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SOLUTION: A point&#8203; P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. The point P is Upper P left parenthesis Sta

SOLUTION: A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. The point P is Upper P left parenthesis Sta