Evaluate cos$(\frac{7\pi}{8}) $. Round your answer to two decimal places.

Question

BlackTom AI · Accepted Answer

We are being asked to evaluate cos(7π/8) and round to two decimals.
First, observe that 7π/8 lies in the second quadrant, where cosine is negative.
Use the identity cos(π − θ) = −cos(θ). Here, 7π/8 = π − π/8, so cos(7π/8) = cos(π − π/8) = −cos(π/8).
Next, recall or compute cos(π/8). A common exact value comes from the half-angle formula: cos(π/8) = sqrt((1 + cos(π/4))/2) = sqrt((1 + √2/2)/2) ≈ 0.923879...
Therefore, cos(7π/8) = −cos(π/8) ≈ −0.923879...
Rounding to two decimal places gives −0.92.
Note: if you instead approximate using a calculator directly for cos(7π/8), you’ll also obtain approximately −0.9239, which rounds to −0.92. If someone rounds differently (e.g., −0.924), you would still commonly report −0.92 when constrained to two decimals.

MUF0091 Mathematics Unit 1 - Semester 1, 2025 12.5 Study Area 2 revision questions

Evaluate cos\((\frac{7\pi}{8}) \). Round your answer to two decimal places.

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