What are the two radians and degrees for the following?
1. tanè=sqrt 3 over 3
Answer: pi/6 or 30deg
What is the other radian and degree?
2. cotè=-1
3. secè=2
4. cscè= sqrt 2
tangene it Positive in the first quadrant, and the third quadrant.
so PI/6 and PI/6+PI or 7PI/6
degrees? 30 and 210
for each one, use the CAST rule to find where else a certain trig ratio is positive or negative
for #1, you have found the angles in quadrant I, but the tangent is also positive in III, (the T of CAST)
So è = 30 degrees in I ---> pi/6
or è = 210 in III ------ 7pi/6
#2
cotè=-1
then tanè=-1 , tan is negative in II or IV
è = 180-45 = 135 ----> 3pi/4
e = 360-45 = 315 ----> 7pi/4
#3
secè = 2
cosè = 1/2 , è will be in I or IV
take over
To find the other radian and degree measures, we will use the trigonometric identities and inverse functions. Let's solve each problem step by step:
1. tan(theta) = sqrt(3)/3
To find the radian measure, we can use the inverse tangent function (arctan):
theta = arctan(sqrt(3)/3)
To find the degree measure, we can convert radians to degrees using the formula:
Degrees = Radians * (180/pi)
Plugging in the value of theta, we get:
Degrees = (arctan(sqrt(3)/3)) * (180/pi)
Degrees ≈ 30°
Therefore, the other radian measure is pi/6 and the other degree measure is 30°.
2. cot(theta) = -1
To find the radian measure, we can use the inverse cotangent function (arccot). However, the inverse cotangent function typically returns values between 0 and pi, so we need to add pi to get the second solution:
theta = arccot(-1) + pi
To find the degree measure, we can convert radians to degrees using the formula:
Degrees = Radians * (180/pi)
Plugging in the value of theta, we get:
Degrees = (arccot(-1) + pi) * (180/pi)
Degrees ≈ 135°
Therefore, the other radian measure is arccot(-1) + pi, and the other degree measure is approximately 135°.
3. sec(theta) = 2
To find the radian measure, we can use the inverse secant function (arcsec):
theta = arcsec(2)
To find the degree measure, we can convert radians to degrees using the formula:
Degrees = Radians * (180/pi)
Plugging in the value of theta, we get:
Degrees = arcsec(2) * (180/pi)
Degrees ≈ 60°
Therefore, the other radian measure is arcsec(2), and the other degree measure is approximately 60°.
4. csc(theta) = sqrt(2)
To find the radian measure, we can use the inverse cosecant function (arccsc):
theta = arccsc(sqrt(2))
To find the degree measure, we can convert radians to degrees using the formula:
Degrees = Radians * (180/pi)
Plugging in the value of theta, we get:
Degrees = arccsc(sqrt(2)) * (180/pi)
Degrees ≈ 45°
Therefore, the other radian measure is arccsc(sqrt(2)), and the other degree measure is approximately 45°.