Trigonometric Function Evaluation

Evaluating Trigonometric Functions

Sine of $2033$

• The initial question involves finding the sine of $2033$. However, the speaker dismisses it, indicating it might be incorrect or requires further review.

Evaluating at $3\pi/2$

• The speaker moves on to evaluate a trigonometric function at $3\pi/2$.
• It's established that $3\pi/2$ corresponds to the point $(0, -1)$ on the unit circle.

Tangent at $3\pi/2$

• The evaluation of tangent at $3\pi/2$ is mentioned.
• Tangent is sine divided by cosine. Here, the values are $-1/0$, so tangent is undefined.

Sine at $2\pi/3$

• The task is to find the sine of $2\pi/3$.
• Sine corresponds to the y-values on the unit circle.
• $\pi/3$ is equal to $60$ degrees.
• $2\pi/3$ or $2 * 60 = 120$ degrees, which lies in the second quadrant.
• In the second quadrant, sine (y-values) is positive.

Cotangent of $13\pi/3$

• The problem involves finding the cotangent of $13\pi/3$.
• Cotangent is the reciprocal of tangent. Given as $1/\sqrt{3}$.
• Rationalizing gives $\sqrt{3}/3$.
• To find the quadrant, we determine where $13\pi/3$ lands.
• The speaker counts around the unit circle in increments of $\pi/3$ to locate $13\pi/3$.