Cosine Functions and Their Properties

The video tutorial explores the cosine graph from -π to 5π, highlighting its periodicity and symmetry. It demonstrates solving for x = 1/2 using cosine's even symmetry and extends this to find multiple solutions by leveraging periodicity. The tutorial generalizes these solutions for any cosine value and addresses handling negative values and inverse functions, emphasizing the importance of understanding the range and periodicity of trigonometric functions.

What is the width of the cosine graph from negative pi to five pi?

• 5 pi

• 3 pi

• 6 pi

• 8 pi

If x equals a half, what is the first solution for the angle?

• pi on 4

• pi on 3

• pi on 2

• pi on 5

What kind of symmetry does the cosine function have?

• Neither

• Even

• Both

• Odd

How do you find additional solutions for a cosine equation using periodicity?

• By adding or subtracting the period

• By multiplying by the period

• By subtracting pi radians

• By adding pi radians

What is the period of the cosine function discussed in the video?

• 2 pi radians

• pi radians

• 3 pi radians

• 4 pi radians

How are even multiples of pi used in finding solutions?

• To find even solutions

• To find no solutions

• To find odd solutions

• To find all solutions

What is the formula for finding solutions when cos x equals k?

• x = 3n pi plus or minus cos inverse of k

• x = 2n pi plus or minus cos inverse of k

• x = n pi plus or minus cos inverse of k

• x = 4n pi plus or minus cos inverse of k

What happens when solving tan x equals negative one?

• Subtract pi over four

• Add pi over four

• Subtract n pi

• Add n pi

What is the range of the cos inverse function?

• Negative pi to pi

• 0 to 2 pi

• Negative 2 pi to 2 pi

• 0 to pi

How do you find solutions for cos x equals negative a half?

• Using 4n pi plus or minus 4 pi over 3

• Using 3n pi plus or minus 3 pi over 3

• Using 2n pi plus or minus 2 pi over 3

• Using n pi plus or minus pi over 3