Find the Exact Value sin((7pi)/4)

Problem

sin((7*π)/4)

Solution

1. Identify the quadrant of the angle (7*π)/4 Since (3*π)/2<(7*π)/4<2*π the angle lies in Quadrant IV.

2. Determine the sign of the sine function in Quadrant IV. In this quadrant, the ycoordinate is negative, so sin((7*π)/4) must be negative.

3. Calculate the reference angle (θ_r*e*ƒ) by subtracting the angle from 2*π

(θ_r*e*ƒ)=2*π−(7*π)/4

(θ_r*e*ƒ)=π/4

4. Evaluate the sine of the reference angle using known trigonometric values.

sin(π/4)=√(,2)/2

5. Apply the sign from step 2 to the reference value.

sin((7*π)/4)=−√(,2)/2

Final Answer

sin((7*π)/4)=−√(,2)/2

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