Find the values of Q in degrees and radians without the aid of a calculator.
a) cotQ = sqrt 3 / 3
b) secQ = sqrt2
a) tan Q = sqrt3
What angle has that tangent? You should know. Consider a 30-60-90 right triangle.
b) cos Q = 1/sqrt2 = 0.707
sin Q would be the same.
What is Q when tanQ = 1?
To find the values of Q in degrees and radians, we can use some trigonometric identities and special triangles.
a) cotQ = sqrt(3)/3
The cotangent function is the reciprocal of the tangent function. So we can find Q by using the arctan function, which is the inverse function of the tangent function.
1. First, find the tangent of Q:
tanQ = 1 / cotQ = 1 / (sqrt(3) / 3) = 3 / sqrt(3) = sqrt(3)
2. Next, find the angle whose tangent is sqrt(3) using a unit circle or a trigonometric table. In this case, the angle Q is 60 degrees or pi/3 radians.
Therefore, the value of Q is 60 degrees or pi/3 radians.
b) secQ = sqrt(2)
The secant function is the reciprocal of the cosine function. So we can find Q by using the arccos function, which is the inverse function of the cosine function.
1. First, find the cosine of Q:
cosQ = 1 / secQ = 1 / sqrt(2) = sqrt(2) / 2
2. Next, find the angle whose cosine is sqrt(2)/2 using a unit circle or a trigonometric table. In this case, the angle Q is 45 degrees or pi/4 radians.
Therefore, the value of Q is 45 degrees or pi/4 radians.