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

Problem

sin(θ)=1,0≤θ≤π/2

Solution

1. Identify the angle θ that satisfies the given condition. In the first quadrant (including boundaries), sin(θ)=1 occurs only at θ=π/2 radians or 90

2. Evaluate the cosine value at this angle.

cos(π/2)=0

3. Evaluate the tangent value using the identity tan(θ)=sin(θ)/cos(θ)

tan(π/2)=1/0

Since the denominator is zero, the tangent is undefined.

4. Evaluate the cosecant value using the identity csc(θ)=1/sin(θ)

csc(π/2)=1/1=1

5. Evaluate the secant value using the identity sec(θ)=1/cos(θ)

sec(π/2)=1/0

Since the denominator is zero, the secant is undefined.

6. Evaluate the cotangent value using the identity cot(θ)=cos(θ)/sin(θ)

cot(π/2)=0/1=0

Final Answer

cos(θ)=0,tan(θ)=undefined,csc(θ)=1,sec(θ)=undefined,cot(θ)=0

Want more problems? Check here!