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:
\(\frac{\sin 26^\circ}{\cos 64^\circ} = \frac{\sin 26^\circ}{\sin 26^\circ}\)Any non-zero number divided by itself equals 1.
\(\frac{\sin 26^\circ}{\sin 26^\circ} = 1\)Final Answer
Therefore, the value of \(\frac{\sin 26^\circ}{\cos 64^\circ}\) is 1.
Similar Questions
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- Value of \(\sin 60^\circ / \cos 60^\circ\)
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Important Questions from Trigonometric Ratios
If \(cosec~\theta =\frac{29}{21}\) where 0 < θ < 90°, then what is the value of 4 sec θ + 4 tan θ?
The value of \(\cot \left( {cose{c^{ - 1}}\frac{5}{3} + {{\tan }^{ - 1}}\frac{2}{3}\;} \right)\)
The distance of the highest point on the graph of the function y = √3 cos x + sin x from the x-axis is:
If A = π / 6 and B = π / 3, then consider the following statements:
I. sin A + sin B = cos A + cos B
II. tan A + tan B = cot A + cot B
Which of the above statements is / are correct?
If \(\sin A = \frac{1}{{\sqrt 2 }}\) and \({\mathop{\rm Cos}\nolimits} B = \frac{{\sqrt 3 }}{2}\), then, find the value of (A + B)º.
A. 60º
B. 75º
C. 105º
D. 90º
