Find the Other Trig Values in Quadrant I tan(theta) = square root of 3

Problem

tan(θ)=√(,3),θ∈Quadrant I

Solution

1. Identify the given value and the quadrant. Since θ is in Quadrant I, all trigonometric functions (sin() cos() tan() csc() sec() cot() are positive.

2. Determine the angle θ Using the known values for special angles, tan(θ)=√(,3) corresponds to θ=60 or θ=π/3

3. Find the sine value.

sin(π/3)=√(,3)/2

4. Find the cosine value.

cos(π/3)=1/2

5. Find the cosecant value by taking the reciprocal of sine.

csc(θ)=1/sin(θ)=2/√(,3)=(2√(,3))/3

6. Find the secant value by taking the reciprocal of cosine.

sec(θ)=1/cos(θ)=1/(1/2)=2

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

cot(θ)=1/tan(θ)=1/√(,3)=√(,3)/3

Final Answer

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

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