Questions: Use the Unit Circle to find the exact value of the trig function. cos(45°) a. 1/2 b. -√3/2 c. √2/2 d. 1

Use the Unit Circle to find the exact value of the trig function. cos(45°) a. 1/2 b. -√3/2 c. √2/2 d. 1
Transcript text: Use the Unit Circle to find the exact value of the trig function. $\cos \left(45^{\circ}\right)$ a. $\frac{1}{2}$ b. $-\frac{\sqrt{3}}{2}$ c. $\frac{\sqrt{2}}{2}$ d. 1
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Solution

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Solution Steps

Step 1: Identify the angle on the Unit Circle

The angle given is \(45^{\circ}\). On the unit circle, \(45^{\circ}\) corresponds to the point \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\).

Step 2: Recall the definition of cosine on the Unit Circle

The cosine of an angle in the unit circle is equal to the x-coordinate of the corresponding point.

Step 3: Determine the cosine value

For \(45^{\circ}\), the x-coordinate is \(\frac{\sqrt{2}}{2}\). Therefore, \(\cos(45^{\circ}) = \frac{\sqrt{2}}{2}\).

Step 4: Match the value with the given options

The value \(\frac{\sqrt{2}}{2}\) corresponds to option c.

Step 1: Identify the angle on the Unit Circle

The angle given is \(45^{\circ}\). On the unit circle, \(45^{\circ}\) corresponds to the point \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\).

Step 2: Recall the definition of cosine on the Unit Circle

The cosine of an angle in the unit circle is equal to the x-coordinate of the corresponding point.

Step 3: Determine the cosine value

For \(45^{\circ}\), the x-coordinate is \(\frac{\sqrt{2}}{2}\). Therefore, \(\cos(45^{\circ}) = \frac{\sqrt{2}}{2}\).

Step 4: Match the value with the given options

The value \(\frac{\sqrt{2}}{2}\) corresponds to option c.

Final Answer

\(\boxed{\frac{\sqrt{2}}{2}}\)

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