Find the Exact Value tan(90 degrees )

Problem

tan(90^∘)

Solution

1. Identify the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

2. Substitute the given angle 90^∘ into the trigonometric functions.

tan(90^∘)=sin(90^∘)/cos(90^∘)

3. Evaluate the sine and cosine values at 90^∘ using the unit circle.

sin(90^∘)=1

cos(90^∘)=0

4. Analyze the resulting fraction.

tan(90^∘)=1/0

5. Conclude that division by zero is undefined in mathematics.

tan(90^∘)=undefined

Final Answer

tan(90^∘)=undefined

Want more problems? Check here!