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Chapter 4: Problem 13

evaluate (if possible) the sine, cosine, and tangent at the real number. $$t=\frac{\pi}{4}$$

Short Answer

Expert verified
The sine of \(t=\frac{\pi}{4}\) is \(\frac{1}{\sqrt{2}}\) or \( \frac{\sqrt{2}}{2}\), the cosine of \(t=\frac{\pi}{4}\) is \(\frac{1}{\sqrt{2}}\) or \( \frac{\sqrt{2}}{2}\), and the tangent of \(t=\frac{\pi}{4}\) is 1.

Step by step solution

01

Calculate the sine of t

Make use of the standard sine value at \( \frac{\pi}{4} \), which is \( \frac{1}{\sqrt{2}} \) or equivalently \( \frac{\sqrt{2}}{2} \) .
02

Calculate the cosine of t

Similarly, utilize the known cosine value at \( \frac{\pi}{4} \), which is also \( \frac{1}{\sqrt{2}} \) or equivalently \( \frac{\sqrt{2}}{2} \) .
03

Calculate the tangent of t

The tangent of t, \( \tan(t) \), can be calculated by dividing the sine of t by the cosine of t. Thus, the \( \tan(\frac{\pi}{4}) \) = \( \frac{sin(t)}{cos(t)} \) = \( \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \) = 1.

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