Questions: Find the values of sin t, cos t, tan t, csc t, sec t, and cot t if P=(sqrt(3)/2, -1/2) is the point on the unit circle that corresponds to the real number t.
sin t=
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Transcript text: Find the values of $\sin t, \cos t, \tan t, \csc t, \sec t$, and $\cot t$ if $P=\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$ is the point on the unit circle that corresponds to the real number $t$.
\[
\sin t=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Solution
Solution Steps
Step 1: Identify the Coordinates
On the unit circle, the coordinates of point P=(0.866,−0.5) directly give us cost=0.866 and sint=−0.5.
Step 2: Calculate ant
Using the definition ant=costsint=0.866−0.5=−0.577.
Step 3: Calculate csct,sect,cott
Using the reciprocal identities, csct=sint1=−0.51=−2 and cott=ant1=sintcost=−0.50.866=−1.732.