Find the Other Trig Values in Quadrant I tan(theta)=1

Problem

tan(θ)=1,θ∈Quadrant I

Solution

1. Identify the given value and the quadrant. Since tan(θ)=1 and θ is in Quadrant I, both sin(θ) and cos(θ) must be positive.

2. Use the definition of the tangent function in terms of a right triangle where tan(θ)=opposite/adjacent Since tan(θ)=1/1 we let the opposite side y=1 and the adjacent side x=1

3. Calculate the hypotenuse r using the Pythagorean theorem r=√(,x2+y2)

r=√(,1+1)

r=√(,2)

4. Determine the sine using the ratio sin(θ)=y/r and rationalize the denominator.

sin(θ)=1/√(,2)

sin(θ)=√(,2)/2

5. Determine the cosine using the ratio cos(θ)=x/r and rationalize the denominator.

cos(θ)=1/√(,2)

cos(θ)=√(,2)/2

6. Determine the cosecant by taking the reciprocal of the sine.

csc(θ)=1/sin(θ)

csc(θ)=√(,2)

7. Determine the secant by taking the reciprocal of the cosine.

sec(θ)=1/cos(θ)

sec(θ)=√(,2)

8. Determine the cotangent by taking the reciprocal of the tangent.

cot(θ)=1/tan(θ)

cot(θ)=1

Final Answer

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

Want more problems? Check here!