Trigonometry: Evaluating sin 26° / cos 64°

The problem asks for the value of the trigonometric expression \(\frac{\sin 26^\circ}{\cos 64^\circ}\). We can solve this using trigonometric identities.

Using Co-function Identities

Notice the relationship between the angles \(26^\circ\) and \(64^\circ\): \(26^\circ + 64^\circ = 90^\circ\). This relationship allows us to use the trigonometric co-function identity, which states that for any angle \(\theta\): \(\cos(\theta) = \sin(90^\circ - \theta)\) Alternatively, we could use \(\sin(\theta) = \cos(90^\circ - \theta)\). Let's apply the identity to the denominator, \(\cos 64^\circ\).

• Substitute \(\theta = 64^\circ\) into the identity \(\cos(\theta) = \sin(90^\circ - \theta)\): \(\cos 64^\circ = \sin(90^\circ - 64^\circ)\)
• Simplify the expression: \(\cos 64^\circ = \sin 26^\circ\)

Simplifying the Expression

Now, substitute the result \(\cos 64^\circ = \sin 26^\circ\) back into the original expression:

Any non-zero number divided by itself equals 1.

Final Answer

Therefore, the value of \(\frac{\sin 26^\circ}{\cos 64^\circ}\) is 1.