Let's start by recalling the Negative Angle Identity for cosine and the Cofunction Identity for tangent that we will use.
Negative Angle Identity
cos (- θ)=cos θ [0.8em]
Cofunction Identity
tan (π/2-θ)=cot θ
To solve the given equation, we will first rewrite it using these identities.
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 first coordinate equal to 0.
As we can see above, the angles whose cosine is 0 are π2 and 3π2.
sin θ=1
We will isolate θ.
sin θ =1 ⇔ θ =sin ^(- 1) 1
Let's use a calculator to find one value for θ.
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 second coordinate equal to 1.
As we can see above, the only angle whose sine is 1 is π2.
