SOLUTION: Solve for 0≤theta≤2π. Give answers to three decimal places, and with π.
1. tan(theta)=-1.5
2. csc(theta)=-1.4
3. 3cot(theta)+4=0
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Question 371500: Solve for 0≤theta≤2π. Give answers to three decimal places, and with π.
1. tan(theta)=-1.5
2. csc(theta)=-1.4
3. 3cot(theta)+4=0
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
For all of these problems, you have been given the function value and you are looking for the angle(s) between 0 and which have that function value. If you know your special angles and their function values, then you should recognize that none of these function values are for the special angles. So we will need to use the inverse trig functions on our calculators to find the reference angles. The inverse trig function buttons on calculators can be difference on different calculators:- Inverse sin: sin-1 or asin or arcsin
- Inverse cos: cos-1 or acos or arccos
- Inverse tan: tan-1 or atan or arctan
Since the range of angles is 0 to , I have to assume that all angles are in radians. So make sure your calculator is set to radian mode for all of the following.
1. tan(theta)=-1.5
Using tan-1(1.5) (We'll handle the negative shortly) we get, rounded to three decimal places: 0.983. Since tan is positive in the 2nd and 4th quadrants we get:
theta = - 0,983 or theta = - 0.983
2. csc(theta)=-1.4
Most calculators do not have a button for inverse csc. So we have to use the fact that sin is the reciprocal of csc (and vice versa). So if the csc of the angle is -1.4, the sin will be 1/-1.4. Using sin-1(1/1.4) (Again we'll handle the negative shortly) we get: 0.796. Sin and csc are negative in the 3rd and 4th quadrants so
theta = + 0.796 or theta = -0.796
3. 3cot(theta)+4=0
First we need to solve for cot. Subtract 4:
3cot(theta) = -4
Divide by 3:
cot(theta) = -4/3
Just like csc, few calculators have a button for inverse cot. So we use the fact that tan is the reciprocal of cot. If cot is -4/3 then the tan is -3/4. Using tan-1(3/4) (we'll deal with the negative in a moment) we get: 0.644. Since tan is negative in the second and 4th quadrants we get:
theta = -0.644 or theta = - 0.644
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