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Draw a reference triangle and find the trig ratio for the angle (if possible) without a calculator.

Draw a reference triangle and find the trig ratio for the angle (if possible) without-example-1
User Vijayant
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Recall the definition of the cosecant function in terms of the sine function:


\csc (x)=(1)/(\sin (x))

Draw the angle -210º in the unit circle to find a reference triangle for that angle:

Notice that a 30-60-90 triangle is formed:

Since the side opposite to the 30º angle has a length of 1/2, then:


\sin (30º)=(1)/(2)

On the other hand, notice that since the angle of -210º lies in the second quadrant, then the value of sin(-210º) is positive:


\sin (-210º)=\sin (30º)=(1)/(2)

Use the definition of the cosecant function to find csc(-210º):


\csc (-210)=(1)/(\sin (-210º))=(1)/(((1)/(2)))=2

Therefore, the value of csc(-210º) is equal to 2.

Draw a reference triangle and find the trig ratio for the angle (if possible) without-example-1
Draw a reference triangle and find the trig ratio for the angle (if possible) without-example-2
User Shefali Aggarwal
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8.4k points

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