csc of 60
Understand the Problem
The question is asking to find the cosecant (csc) of 60 degrees. To solve it, we will recall the definition of cosecant in relation to sine, which is 1/sin(60 degrees). We know the sine of 60 degrees from trigonometric values, so we will use that to calculate cosecant.
Answer
The cosecant of 60 degrees is $\frac{2\sqrt{3}}{3}$.
Answer for screen readers
The cosecant of 60 degrees is $\frac{2\sqrt{3}}{3}$.
Steps to Solve
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Recall the definition of cosecant Cosecant is defined as the reciprocal of the sine function. Therefore, we can write: $$ \text{csc}(60^\circ) = \frac{1}{\sin(60^\circ)} $$
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Find sine of 60 degrees From trigonometric values, we know that: $$ \sin(60^\circ) = \frac{\sqrt{3}}{2} $$
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Calculate cosecant of 60 degrees Substituting the value of $\sin(60^\circ)$ into the cosecant formula gives us: $$ \text{csc}(60^\circ) = \frac{1}{\frac{\sqrt{3}}{2}} $$
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Simplify the expression To simplify the expression, we multiply by the reciprocal: $$ \text{csc}(60^\circ) = \frac{2}{\sqrt{3}} $$
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Rationalize the denominator To present the answer in a conventional format, we can multiply the numerator and denominator by $\sqrt{3}$: $$ \text{csc}(60^\circ) = \frac{2\sqrt{3}}{3} $$
The cosecant of 60 degrees is $\frac{2\sqrt{3}}{3}$.
More Information
The cosecant function is often used in trigonometry, and knowing the basic sine and cosine values allows us to easily calculate it. For reference, the sine of 60 degrees relates to the geometry of a 30-60-90 triangle.
Tips
A common mistake is to forget that cosecant is the reciprocal of sine. Another error is miscalculating or confusing sine values, especially for common angles like 30°, 45°, and 60°.
