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.
(type an exact answer, using radicals as needed. simplify your answer and rationalize the denominator.)
c. tan t = 1
(type an exact answer, using radicals as needed. simplify your answer and rationalize the denominator.)
d. csc t = √2
(type an exact answer, using radicals as needed. simplify your answer and rationalize the denominator.)
e. sec t = √2
(type an exact answer, using radicals as needed. simplify your answer and rationalize the denominator.)
f. cot t =
(type an exact answer, using radicals as needed. simplify your answer and rationalize the denominator.)

Explanation:

Step1: Recall cotangent formula

The formula for $\cot t=\frac{\cos t}{\sin t}$. For a point $P(x,y)$ on the unit - circle corresponding to real number $t$, $\cos t = x$ and $\sin t=y$.

Step2: Identify $x$ and $y$ values

Given the point $P(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ on the unit - circle, $x = \frac{\sqrt{2}}{2}$ and $y=\frac{\sqrt{2}}{2}$.

Step3: Calculate $\cot t$

$\cot t=\frac{\cos t}{\sin t}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.

Answer:

$1$