The real number / corresponds to the point P fraction, if necessary. O: 2 0/6 X 2 x + y = 1 Part 1 of 6 sin t = Continue 6,385 S JUN 6 11 on the unit circle. Evaluate the six trigonometric functions of t. Write your answer as a simplified 6 Sub Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Ces NOO O tv MacBook Air

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 67E
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sin t=
cos t=
tan t= 
csc t=

sec t = 

cot t =

 

### Trigonometric Functions on the Unit Circle

The real number \( t \) corresponds to the point \( P \left( -\frac{5}{6}, \frac{\sqrt{11}}{6} \right) \) on the unit circle. Evaluate the six trigonometric functions of \( t \). Write your answer as a simplified fraction, if necessary.

#### Graph Description
The unit circle is illustrated with its center at the origin \((0,0)\) and radius equal to 1. The circle is defined by the equation \( x^2 + y^2 = 1 \). The point \( P \left( -\frac{5}{6}, \frac{\sqrt{11}}{6} \right) \) is marked on the circle, which lies in the second quadrant where the x-coordinate is negative and the y-coordinate is positive.

#### Required Calculation
Perform the following calculations:

**Part 1 of 6:**
Calculate \(\sin t \)

\[ \sin t = \sqrt{\frac{11}{6}} \ (\frac{\sqrt{11}}{6})\]

Please proceed with the next calculations for the complete evaluation of the trigonometric functions.

### Note:
To submit your answers and verify if they are correct, please use the given user interface. 

Continue for more parts...
Transcribed Image Text:### Trigonometric Functions on the Unit Circle The real number \( t \) corresponds to the point \( P \left( -\frac{5}{6}, \frac{\sqrt{11}}{6} \right) \) on the unit circle. Evaluate the six trigonometric functions of \( t \). Write your answer as a simplified fraction, if necessary. #### Graph Description The unit circle is illustrated with its center at the origin \((0,0)\) and radius equal to 1. The circle is defined by the equation \( x^2 + y^2 = 1 \). The point \( P \left( -\frac{5}{6}, \frac{\sqrt{11}}{6} \right) \) is marked on the circle, which lies in the second quadrant where the x-coordinate is negative and the y-coordinate is positive. #### Required Calculation Perform the following calculations: **Part 1 of 6:** Calculate \(\sin t \) \[ \sin t = \sqrt{\frac{11}{6}} \ (\frac{\sqrt{11}}{6})\] Please proceed with the next calculations for the complete evaluation of the trigonometric functions. ### Note: To submit your answers and verify if they are correct, please use the given user interface. Continue for more parts...
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