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Chapter 5: Problem 6

For each trigonometric function in Column \(I,\) choose its value from Column II. A. \(\sqrt{3}\) B. \(1 \) C. \(\frac{1}{2}\) D. \(\frac{\sqrt{3}}{2}\) E. \(\frac{2 \sqrt{3}}{3}\) F. \(\frac{\sqrt{3}}{3}\) G. \(2\) H. \(\frac{\sqrt{2}}{2}\) I. \(\sqrt{2}\) $$\cos 45^{\circ}$$

Short Answer

Expert verified
H. \(\frac{\sqrt{2}}{2}\)

Step by step solution

01

- Identify the Trigonometric Function's Value

To find the value of \(\cos 45^{\circ}\), use the unit circle or trigonometric knowledge. \(\cos 45^{\circ}\) is a well-known angle in trigonometry.
02

- Recall the Cosine of 45 Degrees

Remember that \(\cos 45^{\circ}\) is equal to \(\frac{\sqrt{2}}{2}\).
03

- Match with Column II

Compare the value of \(\cos 45^{\circ}\) with the values given in Column II. The corresponding value is H. \(\frac{\sqrt{2}}{2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

cosine of 45 degrees
Understanding the cosine of 45 degrees is a crucial part of trigonometry. This specific angle is significant because it results in a simple, well-known value. Cosine, one of the primary trigonometric functions, measures the adjacent side over the hypotenuse in a right-angled triangle.

For an angle of 45 degrees, both the adjacent and opposite sides of the right triangle are equal. Using the Pythagorean theorem, the hypotenuse is \(\frac{1}{\frac{\text{ormalsize{1}}}{\frac{\text{ormalsize{\text{hypotenuse}}}}{\text{ormalsize{\text{value}}}}}}\), which simplifies to \(\frac{\text{ormalsize{1}}}{\frac{\text{Hypotenuse}}{{\text{H}}}}\), \text{which is} \(\frac{1}{\text{ormalsize{\frac{\text{ormalsize{Adjacent}}}{\frac{\text{cos}}{\text{hypotenuse}}}}}}\).\text{ ensures that cosine is}... \text{this results in:

  • Hypotenose definition.
  • It equals \text{lengths of triangle.}
As a result explanation 45 degree angle = equals: For 45 degree function =/( sqrt2/2)

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