<p>Find the reference angles theta for the angles listed below. Find the quadran
ID: 2944043 • Letter: #
Question
<p>Find the reference angles theta for the angles listed below. Find the quadrants in which the angles lie, or identify the angle as quadrantal. Show all the steps for deriving the answer.<br /><br />1.θ= 50 degrees<br />2.θ= 120 degrees<br />3.θ = 300 degrees<br />4.θ = -145 degrees<br />5.θ = -90 degrees<br /><br />Evaluate each of the expressions below without using a calculator, using reference angles and key angle values.<br /><br />6. sin (-90): use the even and odd properties to find the exact value<br />7. cot 5π/4: use the periodic properties to find the exact value</p>Explanation / Answer
Find the reference angles theta for the angles listed below. Find the quadrants in which the angles lie, or identify the angle as quadrantal. Show all the steps for deriving the answer.
1.= 50 degrees = 1st quadrant. reference angle: 50 degrees.
2.= 120 degrees = 2nd quadrant. reference angle: 180-120=60 degrees
3. = 300 degrees = 4th quadrant. reference angle: 360-300=60 degrees
4. = -145 degrees = -145+360=360-145=225 degrees = 3rd quadrant. Reference angle: 225-180=45 degrees
5. = -90 degrees=360-90=270 degrees. Between the 3rd and 4th quadrant. Reference angle: 270 degrees
Evaluate each of the expressions below without using a calculator, using reference angles and key angle values.
6. sin (-90): use the even and odd properties to find the exact value = sin(90+360)=sin(270)=0
7. cot 5/4: use the periodic properties to find the exact value
cot 5/4 = 1/(tan(5/4)) = 1/1 = 1
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