Questions: Find the exact values of the six trigonometric functions of the real number (t). (sin (t)= , csc (t)= ,) (cos (t)= , sec (t)= ,) (tan (t)= , cot (t)=)

Transcript text: Find the exact values of the six trigonometric functions of the real number $t$. \[ \begin{array}{ll} \sin (t)= & \csc (t)= \\ \cos (t)= & \sec (t)= \\ \tan (t)= & \cot (t)= \end{array} \]

Solution

Solution Steps

Step 1: Identify the given coordinates

The provided coordinates are (-20/29, 21/29). These represent (x, y) on the unit circle.

Step 2: Calculate sin(t) and csc(t)

sin(t) is the y-coordinate, so sin(t) = 21/29. csc(t) is the reciprocal of sin(t), so csc(t) = 29/21.

Step 3: Calculate cos(t) and sec(t)

cos(t) is the x-coordinate, so cos(t) = -20/29. sec(t) is the reciprocal of cos(t), so sec(t) = -29/20.

Step 4: Calculate tan(t) and cot(t)

tan(t) = sin(t)/cos(t) = (21/29) / (-20/29) = -21/20. cot(t) is the reciprocal of tan(t), so cot(t) = -20/21.

Final Answer:

sin(t) = 21/29
csc(t) = 29/21
cos(t) = -20/29
sec(t) = -29/20
tan(t) = -21/20
cot(t) = -20/21

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