Question

a point p(x,y) is shown on the unit circle corresponding to a real number t. find the values of the trigonometric functions at t. the point p is p(15/17, 8/17).

Explanation:

Step1: Recall trig - function definitions on unit circle

For a point $P(x,y)$ on the unit circle corresponding to real number $t$, $\sin t=y$, $\cos t = x$, $\tan t=\frac{y}{x}(x
eq0)$, $\csc t=\frac{1}{y}(y
eq0)$, $\sec t=\frac{1}{x}(x
eq0)$, $\cot t=\frac{x}{y}(y
eq0)$.

Step2: Identify $x$ and $y$ values

Given $P(\frac{15}{17},\frac{8}{17})$, so $x = \frac{15}{17}$ and $y=\frac{8}{17}$.

Step3: Calculate sine function

$\sin t=y=\frac{8}{17}$.

Step4: Calculate cosine function

$\cos t=x=\frac{15}{17}$.

Step5: Calculate tangent function

$\tan t=\frac{y}{x}=\frac{\frac{8}{17}}{\frac{15}{17}}=\frac{8}{15}$.

Step6: Calculate cosecant function

$\csc t=\frac{1}{y}=\frac{17}{8}$.

Step7: Calculate secant function

$\sec t=\frac{1}{x}=\frac{17}{15}$.

Step8: Calculate cotangent function

$\cot t=\frac{x}{y}=\frac{15}{8}$.

Answer:

$\sin t=\frac{8}{17}$, $\cos t=\frac{15}{17}$, $\tan t=\frac{8}{15}$, $\csc t=\frac{17}{8}$, $\sec t=\frac{17}{15}$, $\cot t=\frac{15}{8}$