Question

(5 Points) Use the unit circle values to find the value of the trigonometric function. Show all work! csc (****)

Answer 1

Solution:

A unit circle is a circle with radius r = 1 unit

$\small csc\left (- \frac{37\pi }{4} \right )$

$\small \Rightarrow csc\left (- \frac{36\pi }{4}-\frac{\pi }{4} \right )$

sin (-9 - )

So, $\small \theta$ take 4 complete revolution and 1 half revolution in anti-clockwise direction, then it moves pi/4 in same direction. $\small \theta$ stops at $\small 3\pi /4$ position in unit circle.

since  $\small sin\frac{3\pi }{4} = \frac{\sqrt{3}}{2}$

Hence,

$\small \Rightarrow csc\left ( -\frac{37\pi }{4} \right )= \frac{1}{sin\left ( -9\pi -\frac{\pi }{4} \right )} = \frac{2}{\sqrt{3}}$

$\small \Rightarrow csc\left ( -\frac{37\pi }{4} \right ) = \frac{2}{\sqrt{3}}$

XUnit Circle 4号) (0.1) 90°、 (3) 6 09 (59) cose,sino) ( 学) 120- | 1353, 3 150/50 \ 1- 3 (-1,0), soln - - 0 s (10) 2lol "" /330 5n 48領) 3 (3) 200x 亨) 00 (受) (三) 270° (0-1]

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