Find the Other Trig Values in Quadrant I cos(3x)=1

Problem

cos(3*x)=1, in Quadrant I

Solution

1. Solve for the angle by identifying where the cosine function equals 1

cos(3*x)=1

3*x=0+2*π*k

2. Determine the value of x by dividing the angle by 3

x=(2*π*k)/3

3. Identify the solution in Quadrant I by testing integer values for k For k=0 x=0 Since 0 is the boundary of Quadrant I, we check if there are other values. For k=1 x=(2*π)/3 which is in Quadrant II. Thus, the relevant angle for evaluating trigonometric functions is x=0

x=0

4. Evaluate the sine function at the identified angle.

sin(0)=0

5. Evaluate the tangent function using the ratio of sine to cosine.

tan(0)=0/1=0

6. Evaluate the cosecant function, which is the reciprocal of sine.

csc(0)=undefined

7. Evaluate the secant function, which is the reciprocal of cosine.

sec(0)=1/1=1

8. Evaluate the cotangent function, which is the reciprocal of tangent.

cot(0)=undefined

Final Answer

sin(x)=0,tan(x)=0,sec(x)=1,csc(x)=undefined,cot(x)=undefined

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