Exercise 33 Page 963

Let's start by recalling the Cofunction Identity for cotangent that we will use. Cofunction Identity cot (π/2-θ)=tan θ To solve the given equation we will first rewrite it using these identities. Now, we will rewrite tan θ using the Tangent Identity.

We will solve the obtained equations one at a time.

sin θ=0

We will isolate θ using an inverse trigonometric function. sin θ =0 ⇔ θ =sin ^(- 1) 0 Let's use a calculator to find one value for θ.

θ =sin ^(- 1)0

UseCalc

Use a calculator

θ =0

Finally, we need to check if there are any other possible angles that satisfy this equation within the given range. Given Range: 0 ≤ θ < 2π Let's consider the unit circle. Recall that the sine of an angle in standard position is the second coordinate of the point of intersection between its terminal side and the circle. Let's plot all the points on the unit circle with a first coordinate equal to 0.

As we can see above, the angles whose sine is 0 are 0 and π.

cos θ=1

We will isolate θ. cos θ =1 ⇔ θ =cos ^(- 1) 1 Let's use a calculator to find one value for θ.

θ =cos ^(- 1)1

UseCalc

Use a calculator

θ = 0

Finally, we need to check if there are any other possible angles that satisfy this equation within the given range. Given Range: 0 ≤ θ < 2π Let's consider the unit circle. Recall that the cosine of an angle in standard position is the first coordinate of the point of intersection between its terminal side and the circle. Let's plot all the points on the unit circle with a first coordinate equal to 1.

As we can see above, the only angle whose cosine is 1 is 0.