If angle $\theta$ is 135o, evaluate cos$\theta$

Analyze the question: We need the exact value of cos 135°.

Concept: 135° lies in the second quadrant (between 90° and 180°). In this quadrant, cosine is negative (remember "ASTC": only Sine is positive in the 2nd quadrant). To find the value, use the reference angle:

Reference angle = 180° − θ

Solution:

1. Reference angle = 180° − 135° = 45°
2. cos 45° = √2/2
3. Cosine is negative in the 2nd quadrant, so:

cos 135° = −cos 45° = −√2/2

(Check: cos 135° = cos(90° + 45°) = −sin 45° = −√2/2 ✓)

Answer: Option C, −√2/2.

Tip: Memorize the 45° values: sin 45° = cos 45° = √2/2. For angles like 135°, 225°, and 315°, just find the reference angle (45°) and then decide the sign using ASTC (All, Sine, Tangent, Cosine). In the 2nd quadrant, only sine is positive, so cosine and tangent are negative.