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

Problem

sin(3*x)=1, Quadrant I

Solution

1. Solve for the angle 3*x by taking the inverse sine of both sides.

sin(3*x)=1

3*x=arcsin(1)

2. Determine the value of the angle. Since sin(θ)=1 at 90 (or π/2 radians), we set the equation.

3*x=90

3. Isolate x by dividing by 3.

x=30

4. Evaluate the cosine of the angle x

cos(30)=√(,3)/2

5. Evaluate the tangent of the angle x using the ratio of sine to cosine.

tan(30)=sin(30)/cos(30)

tan(30)=1/√(,3)=√(,3)/3

6. Evaluate the cosecant of the angle x as the reciprocal of sine.

csc(30)=1/sin(30)

csc(30)=2

7. Evaluate the secant of the angle x as the reciprocal of cosine.

sec(30)=1/cos(30)

sec(30)=2/√(,3)=(2√(,3))/3

8. Evaluate the cotangent of the angle x as the reciprocal of tangent.

cot(30)=1/tan(30)

cot(30)=√(,3)

Final Answer

sin(30)=1/2,cos(30)=√(,3)/2,tan(30)=√(,3)/3,csc(30)=2,sec(30)=(2√(,3))/3,cot(30)=√(,3)

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