Question 10
Draw a 30-60-90 triangle template. Refer to the diagram below.
We have 1 as the short leg, 2 as the hypotenuse and sqrt(3) as the long leg.
Place the angle theta as the reference angle such that it's opposite the sqrt(3) side.
That allows tan(theta) = sqrt(3)/1 = opposite/adjacent
In other words, tan(60) = sqrt(3)/1
So theta = 60 is one solution. We add on 180 to get the other solution. So the other solution is 60+180 = 240
So tan(60) = tan(240) = sqrt(3)
Answers: 60 and 240
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Question 11a
sin(theta) = -0.8
theta = arcsin(-0.8) or theta = 180-arcsin(-0.8)
theta = -53.1301 or theta = 180 - (-53.1301)
theta = -53.1301 or theta = 233.1301
Add 360 to the first angle to find a coterminal angle counterpart.
-53.1301 + 360 = 306.8699
So the two approximate solutions are
theta = 306.8699 or theta = 233.1301
and those round to 306.9 and 233.1 respectively.
Answers: 233.1 and 306.9
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Question 11b
cot(theta) = 1.8
tan(theta) = 1/(1.8)
theta = arctan( 1/(1.8) ) or theta = 180+arctan( 1/(1.8) )
theta = 29.0546 or theta = 180+29.0546
theta = 29.0546 or theta = 209.0546
theta = 29.1 or theta = 209.1
Answers: 29.1 and 209.1
