Find the Other Trig Values in Quadrant II sin(x)=3/5

Problem

sin(x)=3/5, Quadrant II

Solution

1. Identify the given information and the quadrant. In Quadrant II, the xcoordinate is negative and the ycoordinate is positive.

2. Determine the values of y and r using the definition sin(x)=y/r Here, y=3 and r=5

3. Calculate the value of x using the Pythagorean identity x2+y2=r2

x2+3=5

x2+9=25

x2=16

x=−4

(We choose x=−4 because x must be negative in Quadrant II).
4. Find cos(x) using the ratio x/r

cos(x)=−4/5

5. Find tan(x) using the ratio y/x

tan(x)=−3/4

6. Find csc(x) by taking the reciprocal of sin(x)

csc(x)=5/3

7. Find sec(x) by taking the reciprocal of cos(x)

sec(x)=−5/4

8. Find cot(x) by taking the reciprocal of tan(x)

cot(x)=−4/3

Final Answer

cos(x)=−4/5,tan(x)=−3/4,csc(x)=5/3,sec(x)=−5/4,cot(x)=−4/3

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