4. Robin claims that tan 45° is equivalent to cos 90°. Bradford very adamantly disagrees with Robin and declares that tan 45° is equivalent to cos 0°. Who is correct? Justify your answer.
4. Robin claims that tan 45° is equivalent to cos 90°. Bradford very adamantly disagrees with Robin and declares that tan 45° is equivalent to cos 0°. Who is correct? Justify your answer.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![4. Robin claims that \( \tan 45^\circ \) is equivalent to \( \cos 90^\circ \). Bradford very adamantly disagrees with Robin and declares that \( \tan 45^\circ \) is equivalent to \( \cos 0^\circ \). Who is correct? Justify your answer.
**Justification:**
To solve this, we need to recall the values of the trigonometric functions for specific angles.
1. \( \tan 45^\circ \) is the tangent of 45 degrees. The value of tangent at 45 degrees is known to be 1.
\[
\tan 45^\circ = 1
\]
2. \( \cos 90^\circ \) is the cosine of 90 degrees. The value of cosine at 90 degrees is known to be 0.
\[
\cos 90^\circ = 0
\]
3. \( \cos 0^\circ \) is the cosine of 0 degrees. The value of cosine at 0 degrees is known to be 1.
\[
\cos 0^\circ = 1
\]
Comparing these values:
- Robin claims \( \tan 45^\circ = \cos 90^\circ \) which translates to \( 1 = 0 \), a statement that is incorrect.
- Bradford claims \( \tan 45^\circ = \cos 0^\circ \) which translates to \( 1 = 1 \), a statement that is correct.
Therefore, Bradford is correct. The justification is based on the known values of the trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5ed07d5-7a8f-4097-9c81-82df457ca627%2Fbb337223-d1df-4e83-858c-b9e64dfec461%2Fwie3hos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Robin claims that \( \tan 45^\circ \) is equivalent to \( \cos 90^\circ \). Bradford very adamantly disagrees with Robin and declares that \( \tan 45^\circ \) is equivalent to \( \cos 0^\circ \). Who is correct? Justify your answer.
**Justification:**
To solve this, we need to recall the values of the trigonometric functions for specific angles.
1. \( \tan 45^\circ \) is the tangent of 45 degrees. The value of tangent at 45 degrees is known to be 1.
\[
\tan 45^\circ = 1
\]
2. \( \cos 90^\circ \) is the cosine of 90 degrees. The value of cosine at 90 degrees is known to be 0.
\[
\cos 90^\circ = 0
\]
3. \( \cos 0^\circ \) is the cosine of 0 degrees. The value of cosine at 0 degrees is known to be 1.
\[
\cos 0^\circ = 1
\]
Comparing these values:
- Robin claims \( \tan 45^\circ = \cos 90^\circ \) which translates to \( 1 = 0 \), a statement that is incorrect.
- Bradford claims \( \tan 45^\circ = \cos 0^\circ \) which translates to \( 1 = 1 \), a statement that is correct.
Therefore, Bradford is correct. The justification is based on the known values of the trigonometric functions.
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