If angle θ is 135o, evaluate cosθ

Correct Answer is : −22-{{2}}{2}−22

Correct Answer is : −22-{{2}}{2}−22

Test Index

JAMB Mathematics 2012 Paper

Question : 28

Total: 48

If angle

\theta

\theta

Solution:

Concept:

Cosine is negative in the second quadrant, and

135^\circ

has the same reference angle as

45^\circ

Explanation:

The angle

135^\circ

lies between

90^\circ

and

180^\circ

, so it is in the second quadrant.

In the second quadrant, cosine is negative.

Find the reference angle:

180^\circ - 135^\circ = 45^\circ

Therefore,

\cos 135^\circ = -\cos 45^\circ

Since

\cos 45^\circ = \frac{\sqrt{2}}{2}

, we substitute to get

\cos 135^\circ = -\frac{\sqrt{2}}{2}

Answer:

-\frac{\sqrt{2}}{2}

, which is option C.

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