Find the Other Trig Values in Quadrant I cot(x)=( square root of 3)/3

Problem

cot(x)=√(,3)/3, in Quadrant I

Solution

1. Identify the given trigonometric ratio and the quadrant. Since x is in Quadrant I, all trigonometric functions (sin(x) cos(x) tan(x) csc(x) sec(x) will be positive.

2. Find the tangent value by taking the reciprocal of the cotangent.

tan(x)=1/cot(x)

tan(x)=3/√(,3)

tan(x)=√(,3)

3. Determine the angle x or use the definition of tangent. Since tan(x)=√(,3) in Quadrant I, we know x=60 or x=π/3

4. Calculate the sine and cosine values using the known angle.

sin(x)=sin(π/3)=√(,3)/2

cos(x)=cos(π/3)=1/2

5. Calculate the cosecant and secant values by taking the reciprocals of sine and cosine.

csc(x)=1/sin(x)=2/√(,3)=(2√(,3))/3

sec(x)=1/cos(x)=1/(1/2)=2

Final Answer

sin(x)=√(,3)/2,cos(x)=1/2,tan(x)=√(,3),csc(x)=(2√(,3))/3,sec(x)=2

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