Question

Given that mc006-1.jpg, what is the value of mc006-2.jpg, for mc006-3.jpg?

Answer 1

For
`\(0^\circ < \theta < 90^\circ\)` with
`\(\sin \theta = (21)/(29)\)`, the value of
`\(\cos \theta\)` is
`\((20)/(29)\)`. Therefore, the correct answer is C.

Given
`\(\sin \theta = (21)/(29)\)`, and since
`\(\theta\)` is in the first quadrant (0° <
`\(\theta\)` < 90°), you can use the fact that
`\(\cos \theta = √(1 - \sin^2 \theta)\)` to find the value of
`\(\cos \theta\)`.

`\[ \cos \theta = √(1 - \sin^2 \theta) \]\[ \cos \theta = \sqrt{1 - \left((21)/(29)\right)^2} \]\[ \cos \theta = \sqrt{1 - (441)/(841)} \]\[ \cos \theta = \sqrt{(841 - 441)/(841)} \]\[ \cos \theta = \sqrt{(400)/(841)} \]\[ \cos \theta = \pm (20)/(29) \]`

Since
`\(\theta\)` is in the first quadrant (0° <
`\(\theta\)` < 90°), the cosine is positive. Therefore, the correct answer is:

`\[ \cos \theta = (20)/(29) \]`

So, the answer is C.
`\( (20)/(29) \)`.