Given that $\sin 90°=1$, which statement is true?

• A. $\sin 90°=0$
• B. $\tan 90°=0$
• C. $\cos 90°=1$
• D. $\cos 90°=0$

Answer: (D)

Verified step by step guidance

1. Recall the fundamental values of sine, cosine, and tangent functions at 90 degrees: \(\sin 90^\circ = 1\), \(\cos 90^\circ = 0\), and \(\tan 90^\circ\) is undefined (or approaches infinity).
2. Evaluate each given statement by comparing it to these known values: check if \(\sin 90^\circ = 0\), \(\tan 90^\circ = 0\), and \(\cos 90^\circ = 1\) are true or false.
3. Since \(\sin 90^\circ = 1\) is given and true, the statement \(\sin 90^\circ = 0\) is false.
4. The tangent of 90 degrees is not zero; it is undefined because cosine of 90 degrees is zero, and tangent is sine divided by cosine, so \(\tan 90^\circ\) cannot be zero.
5. The correct statement is \(\cos 90^\circ = 0\), which matches the known trigonometric value for cosine at 90 degrees.